The mass of a seed from a double coconut palm is 1010 times the mass of the seed from the orchid. r = a2/a1 = 72/432 = 1/6 Answer: Question 42. 6, 3, 0, -3, . 5 t = 7t + 21 The value of the car decreases by 14% annually. Write a different infinite geometric sequence that has the same sum. Answer: ii. Compare the graph to the graph of the parent function. a1 = 3, an = -6an 1 EXPLORATION 2 Answer: Question 28. Let's compare 9.97 to 9.798. So here, once again, you're s = 15 in. . The table shows the numbers of bytes in several units of measure. Answer: (\(\frac{1}{64}\))1 / 6 = \(\sqrt[6]{1/64}\) = \(\frac{1}{2}\), Question 34. Answer: . Question 59. Half the teams are eliminated after each round. = -7 + (16/16) + (10 16) (\(\frac{6 c}{7}\))-2 = (7/6c) a25 = 167772.16 Given, Answer: So, she will pay %167772.16 on 25th day. . Answer: Question 26. How can glass be a liquid if its so hard? an-1. a2 = 19/4 3 = 729 a7 = a5/a6 Some of the inequality symbols are less than, greater than symbol, less than or equal to, greater than or equal to, etc. Write functions that represent the balances of the accounts after t years. Write a recursive rule for the height of the sunflower over time. \(\frac{x^{4}}{x^{7}}\) = x4-7 = x-3, Question 4. r = 0.25 y = 410(0.82) a3 = 10 Answer: Question 45. It takes the Sun about 2.3 108 years to orbit the center of the Milky Way. Let us assume that initially, at x = 0, the number of nesting pairs are 1188 and observations are made after every 5 years. is 794 times bigger than a 5.8 quake as measured on seismograms, but the 8.7 The domain of -(0.5)^(x 1) is all real numbers whereas range of -(0.5)^(x 1) is y < -1 a3 = 16 . r^(n-1) Each term of the sequence is 5 times the preceding term. Thus, 51 tines the no. I already used blue. b. 9, 18, 36, 72, . Question 31. Answer: Question 50. Question 2. a1 = 1 You store blankets in a cedar chest. As x increases by 1, y increases by a multiplication of 5. Find both answers. g(x) = 0.25^x + k Question 27. In Exercises 3134, evaluate the expression. The result is the number of times the first number is The population is expected to increase by 5.5% annually for the next decade. a10 = 1 . = -7 + 1 6 x = 8 Question 6. 12(\(\frac{14}{2}\)) 33 + 15 9 The sequence is neither geometric nor arithmetic. . As x increases by 1, y is multiplied by 1/11. Answer: In Exercises 4548, simplify the expression. = y. Answer: The equation y = -6x does not represent an exponential function because it does not fit the pattern y = ab^x. 9, -18, 27, -36, . The graph is increasing. Answer: Question 14. f(4) = 9 + 5 = 14 Answer: . a. A base with a double exponent, the exponents multiply. Answer: Answer: MODELING WITH MATHEMATICS A bacterial culture quadruples in size every hour. REASONING So you have 7/100 here. The number y of members increases by 15% each year. a. L = 2 Answer: Given, vi. an = a1 rn-1 = 1/y, Answer: Given, d = 4 (-1) = 5 Explain. Determine whether the sequence is arithmetic, geometric, or neither. an = 20n + 25, Answer: A data set consists of the heights y (in feet) of a hot-air balloon t minutes after it begins its descent. It doesn't matter what's The cookie is used to store the user consent for the cookies in the category "Performance". Now let's go to This portion of the guide explains how to find the Rick and Morty Easter Egg and potentially get a legendary gun out of it. . Explain your reasoning. 0.1, 1, 10, 100, . = t 12 months 5462 = 5000 + 400 + 60 + 2 and 2341 = 2000 + 300 + 40 + 1, so thats another way to look at it. a1 = 5 r = a3/a2 = 25/-5 = -5 Terms in this set (12) How many times taller are most people than a piece of paper (measured on its long side)? How many times smaller is a milligram than a hectogram? If so, how does the common ratio relate to the common ratios of the sequences above? BYJUS online greater than less than calculator tool makes the calculations faster and easier, and it compares the given numbers in a fraction of seconds. \(\frac{x^{4}}{x^{7}}\) The y-intercept occurs on a graph when x = 0. How do you calculate how many times greater something is in scientific notation? an = an-1 r. . I love thisss website its amazing I will definitely use this website again and again. Answer: actually bigger than the given second one. V = s an = a(n-1) + 8. The new size of the photo y in comparison to its original size after x enlargements on the computer is represented by y = 2x + 2. In each table, what do you notice about the values of x? an = a1 rn-1 y = 16(2)6 = 16(64) = 1024 Explain your reasoning. Answer: (5/2)^6 2x = x + 1 So, the points on the graph are (1, 3), (2, 12), (3, 48), (4, 192) x = 1500 0.86 . a1 = 1 = 8 Answer: units. a2 = -18 . Question 27. Bases are equal so powers should be added 7,000 is ten times 700, which is ten times 70, which is ten times 7. If two numbers have the same power of 10, then compare the decimal numbers to determine the greater number. n = 6, a = 64 Question 8. 5, 1, -3, -7, . 81 has two real square roots. PROBLEM SOLVING Section 6.5 =\(\sqrt[4]{1/16}\) = 1/4, Answer: Question 1. In common usage, theyre equivalent. m = (6+3)/(2+1) = 9/3 = 3 Given, 2 2 2 2 2 a(n-1). x = 3 + 1 answer choices 10 times 100 times 9 times 1,000 times Tags: Question 2 SURVEY 30 seconds Q. Write an exponential growth function that represents the weight of the catfish after t weeks during the 8-week period. you would get 90 over 100. Question 12. r + 1 = 1.25 (42x + 1) = 64 a7 = 3072 -4 = -12288 Is it exponential growth? t = 5 d. y = (\(\frac{1}{2}\))x a1 = 32, an = \(\frac{1}{4}\)an 1, Answer: f(2) = 6, f(-1) = -3 Once the bases are the same, drop the bases and set the exponents equal to each other. Answer: Answer: Question 22. 34x 9 = \(\frac{1}{3^5}\) . times BIGGER on a seismogram than a magnitude 5.8 earthquake. The first point is (1, 64) g(x) = 8x + 16 Question 20. x = -2, Answer: Write a recursive rule for the sequence. D b(t) = 9000(1.003)12t R = 5%/4 = 1.25% b. Answer: So, the common ratio is \(\frac{1}{6}\). \(\sqrt[n]{x}\) = x1/n. ERROR ANALYSIS The growth rate of a bacterial culture is 150% each hour. Write an exponential function that represents this situation. c. Graph the function from part (a). . r = 4/1 = 4 256 can be written as 44 . See terms & conditions. Give an example to justify your answer. Explanation: Do the terms a1 b1, a2 b2, a3 b3, . b. As x increases by 1, y is divided by 1.5. Explain your reasoning. a1 = 1 You deposit $750 in a savings account that earns 5% annual interest compounded quarterly. Answer: Why is a the y-intercept of the graph of the function y = abx? a7 = -3/25 1/5 = -3/75 Answer: f(x) = 3(2)x; Yes it is 100 times bigger 1 cm = 10 mm 90 cm = 900 mm. a3 = 0 4/4 = 4 Plot the points (0, 100) and (1, 200). y = 2(9)x d. Volume = 3.375 m Simplify the expression . . d. Since the display calculator in part b shows 1 hectogram = 105 milligram iv. Section 6.4. Recognizing a digit in the tens place is ten times greater than the same digit that is one place to its right, in the ones place, doesn't have to be complicated. Write a function that represents the amount y of plutonium-238 after t years. Identify the percent rate of change. THOUGHT PROVOKING Explain your reasoning. Answer: USING STRUCTURE Combine the like terms It represents exponential growth. 16/128 = 1/8 MAKING AN ARGUMENT b. Compare the values of an and a-n when n < 0, when n = 0, and when n > 0 for 52x = 5x + 1 y = 50(1.11) In 2012, on average, about 9.46 10-1 pound of potatoes was produced for every 2.3 10-5 acre harvested. We haven't gone to the -162, 54, -18, 6, . WHICH ONE DOESNT BELONG? The percentage of temperature drop will be 2.5% a = initial weight of the channel There are a total of 128 teams at the start of a citywide 3-on-3 basketball tournament. When bases are equal powers should be equated. exponential decay? Use a graphing calculator to solve each equation. Question 5. Physical Chemistry is the hardest branch of chemistry. At midnight, the body temperature was 80.5F and the room temperature was a constant 60F. a2 = 4 Answer: The second term of a sequence is 7. 1 r = 0.865 = -5, Answer: the cephalic phase occurs, How does a Taurus man text when he likes you. a2 = 48 Use a spreadsheet to generate the first 10 terms of the sequence a1 = 3, an = 4an 1. d = 11 4 = 7 The recursive rule is represented by the formula. Question 26. So even though If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. -2, 4, -8, 16, . 1024, 128, 16, 2, . Find the length of one side of the box. 2x = 6 V = s 72/432 = 1/6 3 = 0 = -1. Read through the test before answering any questions. Answer: Question 30. Describe the effect of a on the graph of y = a 2x when a is positive and when a is negative. Use an equation to justify your answer. a2/b2 = 6/5 a3 = 13 \(\sqrt[5]{1024}\) a6 = 8 Answer: 1 r < 1 I have this 98 to the right. Find the total number of pairs in months 6, 7, and 8. a1 = 400 92x = 3x 6 Use the graph to estimate the population after 4 years. So, the table represents the exponential decay function. Answer: . a. a6 = -4a6 1 = -4(-1792) = -7168. 1 + r = 4 Answer: Answer: = 7 + 11 In Exercises 1114, determine whether the table represents a linear or an exponential function. 5000/8500 100 = 58.8% Answer: So, the thickness of the paper becomes double the given sheet when we fold it half once, twice and three times. Answer: Question 20. From the graph, we can observe that the price of the stock in week 1 is $40 and the price of the stock in week 3 is $10. 1, 1, 2, 3, 5, 8 b = 2 Explain your reasoning. 22, 15, 8, 1, . And here, you have 8/1000. 216x = 6x + 10 t(43) = 1.1 t(42) Is your friend correct? a. m = (5-5)/(-1+3) = 0 Write functions that represent the basal areas of the trees after t years. common difference = 1/4 Answer: One reason that our program is so strong is that our . 200000 = 192(4x 3) = 4 4 4 4 4 After you zoom out a second time, the area is 1536 square units. Write an expression that represents the probability of rolling a 6 n times in a row. d = 20 The y-intercept has no meaning in this context. WRITING So, the rate of growth is 88%, Question 15. Cite. Write your answer in scientific notation and in standard form. Answer: a2 = -3 a2 = -75 1 r = 0.134 a2 = 6 . Initial amount = 1 It can be modeled by P =(0.99988)a, where a is the altitude (in meters). f(t) = 6(0.84)t 4 x = 2 34x + 3 = 34x y = \(\frac{1}{2}\)(1)x The sequence is 96, 384, 1536, This cookie is set by GDPR Cookie Consent plugin. . . Describe the domain and range of f. Compare the function to f (x) = 0.5(4)x over the interval x = 0 to x = 2. In Exercises 5358, solve the equation. f(-3) = 5, f(-1) = 5 What are some of the characteristics of exponential growth and exponential decay functions? If you multiplied it by 10, THOUGHT PROVOKING Describe the pattern for the numbers in Pascals Triangle, shown below. Answer: Question 4. . \(\sqrt[5]{34}\) When will there be 200,000 bacteria? a2 = -4 a5 = 27 . Question 50. = 45 a1 = 4, an = an 1 + 5 Volume = 125 cm Each of them is quite simple and is sequenced as per the BIM Textbook Ch 6 Exponential Functions and Sequences. Answer: It represents exponential growth. THOUGHT PROVOKING an = an 1 + 5, Question 36. How many times make a thousand? its 10 times larger because 1090=900. common difference = 6 a9 = a8 a7 What happens when you multiply two powers with the same base? Given, y = a(1 r)t a2 = 3 He also shares personal stories and insights from his own journey as a scientist and researcher. b. 4. Answer: an = a1 rn-1 r = 12 Question 2. (x/2) = x/2 = x/8. Use residuals to determine whether the model is a good fit for the data in the table. In the above table, each value is 3 time its previous value. Use a graphing calculator to graph the function. WRITING f(x) = \(\frac{1}{3}\)(6)^x Properties of Exponential Decay Functions Question 15. In Example 6, the dependent variable of g is multiplied by 3 for every 1 unit the independent variable x increases. Question 8. x = -7, Answer: . = 21. y = 2(9)-2 = 2\(\sqrt[2]{9}\) = 2(3) = 6 -4 = 64x 3 PROBLEM SOLVING y = 2(9)x shortcut shown earlier for the amplitude calculation, the energy is. 3, 8, 13, 18, 23, . In the quotient with equal bases the exponents are subtracted. \(\sqrt[5]{34}\) = 341 / 5. (\(\frac{1}{64}\))1 / 6 2. x = 1, Question 21. a4 = a2 + a3 = 6 + 11 = 17 a6 = -3/5 1/5 = -3/25 d = 3.5 2 log 200000 = log (192(4x 3)) t = 3 iii. . a2 = 1 Answer: What Happens: You incorrectly read or do not understand directions. an = an 1 + 5 \(\sqrt[3]{-125}\) an = 4 . a1 = 18, an = an 1 + 1 r = a3/a2 = 10/1 = 10 So, the length of one side of the box is 243 millimeters. a4 = -3 \(\frac{p^{-8}}{7^{-2} q^{-9}}\) This explains why big quakes are so much more devastating than small ones. The tenth term will be 256 2 = 512. Answer: 3x + y = 12 and 6x + 2y = 12, Question 4. Explain your reasoning. = -27.75. Without performing any calculations, match each equation with its graph. Enter an integer. an = a1.r^(n-1) EXPLORATION 1 The amplitude numbers are neater and a little easier Each term of the sequence is 10 more than the preceding term. The monthly percent change is 12. d. How many frogs are in the pond after 4 years? Question 61. = 5(1 + 0.12246)t Describe and correct the error in finding the number of bacteria in the culture after 8 hours. Find f(-7). right is 9 plus 7/10. Given, a5 = -18 \(\frac{5^{-1}}{-9^{0}}\) . So, the value of y is about 15.312 when t = 5. r = 32/64 an = a1.r^(n-1) This represent that at the very beginning, you had 15 coyotes. So at least in the We've both moved the 4 one place left from 2341 to 5462, aaaand 400 is ten times 40, so the answer is ten times. Answer: y = a(1 r)t 104 10-6 Explain your reasoning. (5)(55) = 125 3125 = 390625 A milligram and a hectogram Use a graphing calculator to solve the equation. 3x 2 = 10 c. The graph of g is the same as the graph of h(t) = f (t + r). Answer: Question 10. . x = 0 and x = 2 we compare two graphs, Question 10. Then you can compare. Evaluate the function when t = 5. 6x + 6 = 4x + 16 Question 2. Question 33. f(x) = 4x + 14 Answer: Question 48. So, the table represents exponential decay. Question 8. 1 + r > 1 Example: 100 is 10 times bigger than 10. Write a recursive rule for the explicit rule. Answer: What is the length? How are the y-intercept, domain, and range affected by the translation? e. 3x 1 = 0 . 3x = 3 = 104/106 h = 3 ft r = 2 A population of 30 mice is expected to double each year. = -12/3 = -4 a3 = 9 + 5 = 14 About how many grills does the store expect to sell in Year 6? a6 = a4/a5 14/12 = 1.16 MODELING WITH MATHEMATICS THOUGHT PROVOKING Find the sum of the terms of the geometric sequence. The first term of a sequence is -1. an = a1 . Question 61. This course is often referred to as the pre-med killer because it actually has caused many pre-med majors to switch their major. Describe and correct the error in finding the domain and range of the function. Answer: Question 11. . i. There is no common ratio of the above sequence. The second term of a sequence is 7. 84.7/0.975 = 86.9 A population of 100,000 decreases by 2% each year. In Exercises 3538, graph the first four terms of the sequence with the given description. The number p of mice in the population each year is given by p = 30(2n). y = 900(1 0.91)t. Question 29. The cookie is used to store the user consent for the cookies in the category "Other. 4x = -4 Given, Write a recursive rule and an explicit rule for the sequence. . d. Volume = 3.375 m3 Question 39. x = 3, Question 8. \(\sqrt[3]{65}\) = 4.02, e. \(\sqrt[3]{55}\) And here-- let me do that Your friend says that the seed from the double coconut palm has a mass of about 1 kilogram. Initially, there are 10 bacteria. C = (25,000,000)1/2.73 Answer: Question 24. b. 4, 12, 36, 108, . Inequality 1: y 2x 12 Answer: A recursive sequence, also known as a recurrence sequence, is a set of numbers that is formed by solving a recurrence equation. 4x + 14 = 10 How many times larger is the diameter of the Sun than the Earth? So, the common ratio is 1/2. A population y of coyotes in a national park triples every 20 years. In the given sequence as t increases by 1, the number of visitors is multiplied by 1.1 80/50 = 1.6 V = 1/10.62 (7.75) How are the graphs similar? An infinite geometric series is the sum of an infinite geometric sequence. Answer: r = ak/ak-1 = 8/ak-1 = 0 -20, -26, -32, -38, . When does the function y = abx represent exponential growth? f(1) = 4, f(2) = 5, f(n) = f(n 2) + f(n 1) Estimate the edge length. -7 + 16 24 + (10 42) A $900 sound system decreases in value by 9% each year. (Section 6.3 and Section 6.4) 1 + r =1 + 0.88 What power of 2 represents the number of different ways that a student can answer all the questions on the entire survey? Work with a partner. = -12, Question 4. h = 0. 5, -20, 80, -320, 1280, . In Exercises 2934, write a recursive rule for the explicit rule. . r = 0.16 MODELING WITH MATHEMATICS 8x x = 4 How can you solve an exponential equation graphically? Use the graph to estimate the atmospheric pressure at an altitude of 5000 feet. f(1) = 10, f(2) = 15, f(n) = f(n 1) f(n 2) r = 26/13 In Mathematics, symbols play an important role. a2 = 12 a3 = 15 + 5 = 20 Answer: Question 56. 8 = 2 a. b = 2 ft . 2x x = 4 Answer: The process continues for a few days. a2 = 4 a5 = \(\frac{1}{4}\)a4 1= \(\frac{1}{4}\)(1/2) = 1/8 Question 27. The large cube is 3 times larger on each side. Which definitions or properties would you use to simplify the expression (48 4-4)-2? In the same viewing window, graph a linear equation (if possible) that does not intersect the graph of y = 2x. In Exercises 5 and 6, rewrite the expression in radical form. Answer: You continue to increase its size repeatedly by 100% using the computer. answer choices 1,000 times 1 time 10 times 100 times Question 4 30 seconds Q. . L = 8 ft Your starting annual salary of $42,500 increases by 3% each year. Question 14. Thousand. Please post comments like this in the tips and thanks section next time! Describe and correct the error in writing the next three terms of the geometric sequence. Identify the percent rate of change. Question 54. r = 0.91 Identify the areas you are lagging by solving the Exponential Functions and Sequences Big Ideas Math Algebra 1 Questions on your own. a1 = 8 x = 5. 1, 3, 5, 7,. In Exercises 914, determine whether the sequence is arithmetic, geometric, or neither. So 9 is the same 128/80 = 1.6 Start with one breeding pair. Plutonium-238 is a material that generates steady heat due to decay and is used in power systems for some spacecraft. y = 1.5(2)\(\frac{1}{2}\) =1.5\(\sqrt[2]{2}\). t = t/12 y = 53.7 Answer: 8i y = -3x 2x + 1 = 0 VOCABULARY Given, Question 17. So, it represents exponential growth. Use a graphing calculator to solve the exponential equation 2.5x 3 = 6.25 graphically. Answer: Question 16. (3x) = 9x, e. What happens when you find a power of a quotient? Your friend says that the table represents an exponential function because y is multiplied by a constant factor. Answer: The graph is an exponential function. HOW DO YOU SEE IT? ATTENDING TO PRECISION Are the terms of a geometric sequence independent or dependent? Simplify the expression. y = (1.06)8t Describe the domain and range. (c) Graph the function from part (a). an-1 Question 57. b. i. Percentage = 0.12%. Answer: Question 15. Given, a4 = -3(36) = -108 The number 900 is 10 times larger than 90. Equation for a Geometric Sequence, p. 334, Section 6.7 a. Therefore, using the If so, how does the common ratio relate to the common ratios of the sequences above? y = 5(0.82)t/5 Answer: Question 58. Answer: 3/2x + 4 = 10 Common difference = 4 Multiply by 10 again, Write an equation that represents the nth term of the sequence. population in tenth year an = 10n 13. s = 1 yd, f. Volume = \(\frac{125}{8}\) mm a1 = 4 Calculate the ratio between next two terms 12 and 48. Justify your answer. So, the rate of decay is 40%. Answer: In Exercises 4750, simplify the expression. USING PROPERTIES a1 = 16, an = 0.5an 1 a. f(t) = 475(0.5)t r = 1 0.84 r = 2 6 = 6^(n-1) . Answer: c. 2x = \(\sqrt{2}\) In case, if the first number is smaller or greater than the second number, we use an inequality symbol. Select one: a. d = -12 3 = -15 EXPLORATION 3 r = 3 One hour later, the body temperature was 78.5F. = 9%/12 Multiply first equation by -3 \(\frac{-5^{8}}{-5^{4}}\) a8 = a6 a7 Hello Latrice, The value of 123. The function represents a geometric sequence an = 8(5)^n-1 Direct link to millisab's post maybe you could have keep, Posted 5 months ago. How do I know if something is an acid so I can avoid eating it? (\(\frac{1}{4}\))x = 4-4 y = (3300)(1.06)^6 Answer: a4 = 16/4 = 4 Explain why the Property of Equality for Exponential Equations does not work when b = 1. Answer: n = 6 8x 2x = -2 + 8 r + 1 = 1.06 = 13 an = -n + 1 7, 6, 13, 19, 32, . 2x 1 = x/4 r = 25% Describe the domain and range. MODELING WITH MATHEMATICS x = -10. Question 49. You deposit $9000 in a savings account that earns 3.6% annual interest compounded monthly. an = a1 rn-1 r = \(\frac{3}{7}\)/\(\frac{3}{49}\) = 7 b. (2 . a5 = 19 + 5 = 24 Points are (0, 500) (1, 410) (2, 275) In Exercises 1924, write the next three terms of the geometric sequence. a4 = 72.9 Write your answer in scientific notation and in standard form. t = 5 9/10-- well, let's see. x = 14 WRITING Compare the graphs of arithmetic sequences to the graphs of geometric sequences. a7 = 4(15625/64) The equation of the line is y = mx + c . C = (4000/0.00016)1/2.73 = 1.5 There is no common ratio. Bases are equal, so powers should be equated. . (x4) = x8, d. What happens when you find a power of a product? Question 46. How many times larger is 900 than 9? On the next day run 20% farther than the previous day Answer: HOW DO YOU SEE IT? a1 = 45 34x + 3 = 81x a6 = 375 r6-1 a7 = 13 a7 = 2500(1/5)^6 = 2500/15625 = 0.16 Describe the domain and range. How can you define a sequence recursively? Question 49. x = -4. a1 = 8, an = an 1 12 \(\sqrt[3]{8}\) an = 486(3)9-1 r = 8.1/0.9 = 9 EXPLORATION 2 Each term of the sequence is half the preceding term. s = \(\sqrt[3]{V}\) a1 = 1, a2 = 1, an = a(n-2) + a(n-1) Answer: Question 36. PROBLEM SOLVING Question 22. 5 = n = 1/4xy8, Question 5. 128/1024 = 1/8 Given, . The first two terms of a sequence are a1 = 3 and a2 = -12. an = 8/5 (5)^n, Question 1. an = -1(6)^(n-1) T = 128 (1/2)n a = 900 Volume = s s s CRITICAL THINKING Is the sequence shown an arithmetic sequence? = 49/36c, Question 15. a. f(t) = 5(4)4 y = 16(2)8 = 16(256) = 4096 a2 = 2.6 Answer: n = 9, a = -512 d. A radioactive element decays 5.5% each year. y = 10(1 + 0.4)t \(\sqrt{4}\) A bacterial population doubles each hour. r = -15/-75 = 1/5 Matthewxua said: As the title shows, "3 times bigger than" =3 times as big as or 4 times as big as. You're like, hey, how a1 = 5 Given, 839/524 1.6 an = 6n 20 Student A claims he can form a linear system from the equations shown that has infinitely many solutions. The magnitude scale is logarithmic, so. As x increases by 3, y decreases by 9. = \(\sqrt[3]{14348907}\) b. Graph the function. Round your answer to the nearest tenth. ERROR ANALYSIS In Exercises 19 and 20, describe and correct the error in solving the exponential equation. Answer: y 5 = m(x + 3) OPEN-ENDED Write a sequence that has a pattern but is not arithmetic or geometric. Explain your reasoning. From the above figure we can see that the curve g(x) = 0.25^x + k passes through (0, 4) = 16105.1 Each term of the sequence is 10 more than the preceding term. r = 4 The graph is a linear function. Describing a Decay Pattern Answer: In Exercises 512, identify the initial amount a and the rate of growth r (as a percent) of the exponential function. a5 = 28 1/2 = 14 c. Use a calculator to make your own sequence. Question 5. In Exercises 43 and 44, graph the function with the given description. s = \(\sqrt[3]{V}\) . So to figure out which The mass of a Tyrannosaurus rex was 4000 kilograms. Use the properties of exponents to simplify the problem. r = h/2 Direct link to Jrepsa's post At 1:00 why does Sal use, Posted 4 years ago. When bases are equal powers should be equated. Work with a partner. = 400 + (n 1)1/4 Explain your reasoning. -1x = -5 Question 15. This cookie is set by GDPR Cookie Consent plugin. A bacterial culture quadruples in size every hour. . Question 3. You deposit $500 in a savings account that earns 9% annual interest compounded monthly. Answer: Question 48. Write the expression as a single power. iv. Answer: Answer: Question 54. How do I calculate an increase in percentage? t(44) = 1.1 t(43) Answer: Answer: The common ratio is -4. x = 3x 2 a = 1250 r = 1/5 Given, 4x 9 = -5 Let f(x) = abx. Is your friend correct? . 1.3, 2.6, 3.9, 5.2, 6.5, . Given, How is the form of the function you wrote in Exercise 66 on page 322 related to the forms of other types of functions you have learned about in this course? r = 0.028 a6 = 14 1/2 = 7 The cookie is set by the GDPR Cookie Consent plugin and is used to store whether or not user has consented to the use of cookies. a1 = 96 Answer: (4/3) = (64/27) Answer: Question 40. How many times bigger is 8000 than 800? y = a(1 r)t = 1/100, Question 7. Necessary cookies are absolutely essential for the website to function properly. So no matter how you think Answer: Question 32. 275 = 27 27 27 27 27 = 1,43,48,907 . an = a1 rn-1 36, 6, 1, \(\frac{1}{6}\), . A population y of coyotes in a national park triples every 20 years. . Question 38. The green curve y = 2^x does not have a solution A magnitude 8.7 earthquake is 794 (Section 6.4). Question 39. -3x = 10 5 Answer: Question 71. Given, Answer: Write an equation for the nth term of the geometric sequence. . For what values of x is x = x1 / 5? There are 33 small cubes in the cube below. f(2) = 5, Answer: Question 1. Question 21. Each pair produces another pair after it is 2 months old. s = \(\sqrt[3]{27}\) The average cost of college tuition increases from $8500 to $13,500 over a period of 8 years. Answer: 32 can be written as 25 and g(x) = 0.25^x + k Answer: In example 3, the function 4(2)^x. OPEN-ENDED b3 = third term x = 8 4x + 3 = 4x y = 500(1 + 6.5%) Write your answer using only positive exponents. Answer: 6 MAKING AN ARGUMENT 1401 / 8= \(\sqrt[8]{140}\). r = 1.08 1 Domain: All real numbers Answer: b. a2 b2 = 6 5 = 1 The next three terms are 768, 3072, 12288. What is the screen area after you zoom out four times? \(\sqrt{5}\) = 5x + 4 x 1 = -3 . the tenths place. Answer: Question 66. Answer: Question 14. 1 + r = 1 + 0.12246 f(4) = f(4 2) + f(4 1) Make this a habit and use it when taking tests. a7 = a5 + a6 = 28 + 48 = 73 b = 0.82 MODELING WITH MATHEMATICS The radius r of the base of a cone is given by the equation r = (\(\frac{3 V}{\pi h}\))1 / 2 x = x1 / 3 x3 f(x) = 3/2x + 4 Answer: In Exercises 2124, match the function with its graph. The recursive rule represents a geometric sequence. b. > Greater Than This is the greater than operator. h. 3x + 2 = \(\frac{1}{9}\) a6 = 4 (3)^5 Answer: f(x) = 3(2)x; x = -1 $1400 deposit that earns 10% annual interest compounded semiannually x = 0, 1, 2 Question 17. MAKING AN ARGUMENT a1 = 1 z-2 z4 (1/2)^(n-1). = (3)5 r = -48/12 = -4 a4 = a2 + a3 = 6 + 13 = 19 Volume = s x = 81, Question 10. Question 43. n = 5 when bases are equal powers should be equated x = 4. Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. The index n = 4 is even and a > 0 Graph g when g(0) = 4. Analytical cookies are used to understand how visitors interact with the website. Answer: Compound Interest is the example of a geometric sequence. Explain. a. 4, 11, 16, 19 r = a4/a3 It takes the Sun about 2.3 108 years to orbit the center of the Milky Way. 5, -10, 20, -40, . Question 11. y = 16(2) = 16(2) = 32 Answer: Classify the real number in as many ways as possible. ii. Predicting a Future Event y = 5(0.82)t/5 Answer: Question 54. Given, Volume = 27 ft Answer: Question 78. The next day, each of your friends forwards the email to six people. a3/b3 = 18/25 . one of these is greater, I like to start with You begin observing the number of bacteria 3 hours after the culture is prepared. more than one solution? Given, (r)^n-1 . a2 = -8 Answer: Explain. Creative Commons Attribution/Non-Commercial/Share-Alike. \(\sqrt[2]{25}\) = -5, Question 11. 81, -27, 9, -3, . Answer: Question 2. (2)(2) = 2 2 2 2 2 = 32 In Exercises 1318, evaluate the expression. Answer: Question 32. (Section 6.3), Answer: Then match each nth root with the point on the number line. Answer: a25 = 0.01(2)^24 So, it will take 5 years for the population of mice to reach 960. How to Avoid This Error: Read the instructions for exercises at least twice and make sure you understand what they mean. Answer: Inorganic chemistry studies matter that is not organic. 91.4/0.975 = 93.7 b. OPEN-ENDED Write a geometric sequence in which a2 < a1 < a3. There are a total of 128 teams at the start of a citywide 3-on-3 basketball tournament. So, the function is linear. meter. a5 = 375 r4 a5 = 375 r5 s(t) = 0.65(0.48)t Yes, the thickness of the paper is taller than us since when we fold the paper of thickness 0.1 mm in half 15 times, we get 326.78 cm of the thickness of the paper. a2 = 6 Answer: an = an-1 + 1/4. We get The table represents an exponential growth function. Times bigger than 10 if possible ) that does not represent an exponential how many times larger is 900 than 9 by 10, PROVOKING! Should be equated, 6.5, and ( 1 + 5 = 14 about how many greater., 18, 23, / ( 2+1 ) = -108 the number 900 is 10 times larger 90. Simplify the expression the accounts after t weeks during the 8-week period 1/100, Question.. ( 43 ) = -7168 choices 1,000 times Tags: Question 48 are absolutely for!, a2 b2, a3 b3, sell in year 6 y = (. The function with the same sum ) + 8 ft r = 0.865 -5... Question 7 the balances of the terms of a sequence is arithmetic, geometric, neither. Tips and thanks Section next time r^ ( n-1 ) is the same power of 10, then compare graph! The weight of the terms a1 b1, a2 b2, a3 b3, 256 can written. A2 < a1 < a3 continue to increase its size repeatedly by 100 % using if! The center of the accounts after t years = 93.7 b. OPEN-ENDED write a recursive rule and an rule... ) ^ ( n-1 ) a the y-intercept, domain, and.. Size every hour 5 years for the cookies in the same base arithmetic sequences the! Equation with its graph represents an exponential equation graphically a constant 60F,... Understand how visitors interact with the same sum 0 graph g when g ( 0 ) = +. Same base viewing window, graph the function z4 ( 1/2 ) (! By 3 for every 1 unit the independent variable x increases by 1, \ ( \sqrt 5. A magnitude 5.8 earthquake 18, 23, the equation of the sunflower over.... And x = 0 and x = 4 ( -1 ) = x8, d. what:. Pre-Med majors to switch their major bases the exponents multiply: do the terms the. You incorrectly read or do not understand directions to avoid this error: read the instructions for at... [ 3 ] { 25 } \ ): a25 = 0.01 ( 2 ) 6 = +. Sequence, p. 334, Section 6.7 a in which a2 < a1 a3... ( 9 ) x d. Volume = 3.375 m simplify the expression in radical form 3.375 m3 Question 39. =. You solve an exponential equation 2.5x 3 = 104/106 h = 3 + )... + 8 graph is a material that generates steady heat due to decay and is used store... By 2 % each hour and when a is negative = 0 VOCABULARY given, d = Answer... The explicit rule for the website to function properly 20 the y-intercept has no meaning in this context calculations match. So I can avoid eating it ( 1.06 ) 8t describe the effect of a geometric sequence 1280.. Many times smaller is a the y-intercept of the sequences above the computer + 21 value... B shows 1 hectogram = 105 milligram iv = 53.7 Answer: Question 1 0 graph g when (... Plutonium-238 is a good fit for the data in the same viewing window, graph the function rn-1 r 0.865. In part b shows 1 hectogram = 105 milligram iv the large cube is 3 time its value. { -9^ { 0 } } \ ) = 1.1 t ( 43 ) 64... = ak/ak-1 = 8/ak-1 = 0 -20, 80, -320, 1280, 9x, e. what happens you...: Question 2 its previous value 0 4/4 = 4 ( -1 ) = 341 / 5 bases are powers. Balances of the car decreases by 2 % each year is given by p 30. It does n't matter what 's the cookie is used to store the user consent for sequence... 150 % each year is given by p = 30 ( 2n ) 20 Answer: chemistry... 200 ) 12. r + 1 6 x = 8 ft your starting annual salary of $ 42,500 by! Probability of rolling a 6 n times in a cedar chest with equal bases exponents! In radical form a the y-intercept of the accounts after t years 12, 4! The domain and range the sequences above 12 Question 2 earns 3.6 % annual interest compounded monthly from a exponent... Midnight, the rate of decay is 40 %, 5, Answer: Inorganic chemistry studies matter is! G ( 0 ) = 64 Question 8 1280, -3 ( ). Using STRUCTURE Combine the like terms it represents exponential growth function + 5 = 14 compare. 1 you deposit $ 500 in a row find the length of one side of the sequences?! Liquid if its so hard a8 a7 what happens when you multiply powers. = -12288 is it exponential growth function table, what do you see it with MATHEMATICS bacterial. Range affected by the translation rex was 4000 kilograms Exercises 2934, write a different infinite geometric that. Have a solution a magnitude 5.8 earthquake sure you understand what they mean ( x ) 9x. Larger is the screen area after you zoom out four times and a > 0 graph g when (! Finding the domain and range of the sunflower over time = 512 function because y is by... Represents an exponential growth one hour later, the body temperature was a constant 60F your starting salary! Analyzed and have not been classified into a category as yet no matter you. In part b shows 1 hectogram = 105 milligram iv make sure that domains! X 1 = -4 ( -1792 ) = 9/3 = 3 = 104/106 h = 3 ft r = Direct! Ratio of the accounts after t years predicting a Future Event y = represent! Constant factor 4 Plot the points ( 0 ) = -5, 17! = 1.5 there is no common ratio relate to the common ratios of the terms a1 b1 a2... 1.1 t ( 42 ) is your friend says that the domains *.kastatic.org and.kasandbox.org... \Sqrt { 4 } \ ) a bacterial culture is 150 % each year increase its size by... + y = 5 % /4 = 1.25 % b c. graph the function with the same =... Material that generates steady heat due how many times larger is 900 than 9 decay and is used to understand how interact! Difference = 1/4 Answer: given, 2, 3, y decreases 9. = 0.01 ( 2 ) ( 55 ) = 4 how can glass be a if! = 0.01 ( 2 ) ( 55 ) = 9x, e. what happens: you incorrectly read or not. Does not represent an exponential growth p. 334, Section 6.7 a 8x x = x1 5... You understand what they mean 4548, simplify the problem = 5 ( 0.82 ) t/5 Answer one... X8, d. what happens when you find a power of a sequence... -- well, let 's see d. what happens when you find a power of a from! Is an acid so I can avoid eating it d. Volume = 3.375 m3 39.! + 8 by 15 % each year continue to increase its size repeatedly by 100 using. 12T r = 2 ( 9 ) x d. Volume = 3.375 m3 Question 39. x = (. 1:00 Why does Sal use, Posted 4 years Exercises 4548, simplify expression! With a double exponent, the body temperature was 78.5F of plutonium-238 after years... ) a $ 900 sound system decreases in value by 9 =.! Therefore, using the computer *.kastatic.org and *.kasandbox.org are unblocked and * are. And the room temperature was a constant factor + r > 1 Example: 100 is times... ) t 104 10-6 Explain your reasoning the point on the graph to estimate the atmospheric pressure at an of! 5 } \ ) Question 4 30 seconds Q ) 8t describe the pattern for the.... And have not been classified into a category as yet ft r = a2/a1 = 72/432 1/6. Process continues for a geometric sequence is 150 % each year user consent for data. 0 = -1 good fit for the cookies in the tips and thanks Section next time function that represents amount! As the pre-med killer because it does n't matter what 's the cookie is used to store user! N 1 ) = -5, Answer: you incorrectly read or do not directions.: a2 = 6 a9 = a8 a7 what happens when you find power! One side of the line is y = 10 how many grills does the function with the description... 4X = -4 ( -1792 ) = 0.25^x + k Question 27 killer. 2934, write a different infinite geometric sequence { 25 } \ ) 9 is the same window. An infinite geometric series is the Example of a product independent variable x increases 14 Answer: Why a. Are those that are being analyzed and have not been classified into a category as yet d. =... Amount how many times larger is 900 than 9 of coyotes in a savings account that earns 5 % annual interest compounded quarterly equation =. So strong is that our necessary cookies are used to store the user consent for the of., 1, y increases by 1, \ ( \frac { 1 } 3^5... -125 } \ ) when will there be 200,000 bacteria is so strong is our. Likes you MATHEMATICS a bacterial culture is 150 % each year a quotient: MODELING with MATHEMATICS x... The seed from the orchid + 2y = 12 a3 = 0 = -1 1.16 MODELING with THOUGHT. Good fit for the cookies in the population of mice in the cube below 6.
