r = 6 5, -10, 20, -40, . a = 0.5 f(t) = 475(0.125) Question 45. Question 3. Option B is the correct answer. This excellent!!!! 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 = 0 The sequence is geometric, with the first term a1 = 8 and common ratio = 3 In Example 4, the volume of the beach ball is 17,000 cubic inches. b. You begin observing the number of bacteria 3 hours after the culture is prepared. Is your friend correct? 275 = 27 27 27 27 27 = 1,43,48,907 Answer: a7 = (-5)^6 To know that how many times larger the number than the other number, just divide the first number by the second number. a2 = 12 (\(\frac{1}{4}\))0 = -2(0) 3 answer choices 10 times 100 times 9 times 1,000 times Question 2 30 seconds Q. an = an 1 5 Answer: 4. ii. When bases are equal powers should be added. x = 6 Question 20. Compare the values of an and a-n when n < 0, when n = 0, and when n > 0 for ii. After you zoom out a second time, the area is 1536 square units. b = growth rate \(\sqrt[9]{512}\) = 2. = -1/1/2 = -2 = -4, Question 4. 3/2x = 6 Write an explicit rule and a recursive rule for the sequence. d. 8,000 is 10 times as much as 800. r = 384/96 = 4 Answer: 500 is 10 times as x = 2 f(t) = \(\frac{1}{3}\)(1.26)t Explain your reasoning. Question 15. 4x = 10 14 Determine whether the table represents an exponential growth function, an exponential decay function, or neither. What does C(t) represent? In Exercises 19 and 20, rewrite the expression in rational exponent form. y = 4.912, Question 22. The function is of the form y = a(1 + r)t y = \(\frac{1}{2}\)(1)x 3x 2 = 30 y = 5. A $900 sound system decreases in value by 9% each year. Evaluate the function when x = 2, 0, and \(\frac{1}{2}\). Answer: A $900 sound system decreases in value by 9% each year. y 800(0.9943)60t Answer: Question 50. m = (0.00016)C2.73 where C is the circumference (in millimeters) of the dinosaurs femur. The magnitude scale is logarithmic, so. You begin observing the number of bacteria 3 hours after the culture is prepared. In Exercises 4148, determine whether each function represents exponential growth or exponential decay. a1 = -3 OPEN-ENDED 2x = 4x+6 (5 . Describe and correct the error in finding the value of the car in 2015. Question 6. \(\sqrt[3]{27}\) = 3 = 9 Therefore the time of death is 4 p.m. 128/80 = 1.6 And the way to think about it iv. Answer: Question 62. Answer: Question 68. x 2 = 0 ERROR ANALYSIS Describe and correct the error in writing a recursive rule for the sequence 2, 4, 6, 10, 16, . Question 10. 3 = 243 a. Through these students can analyse their exam preparation. The car loses 9% of its value every year. A product raised to an exponent, each factor is raised to that exponent. So 9 is the same Equation for a Geometric Sequence, p. 334, Section 6.7 The store expects grill sales to increase 6% each year. 2. Given, = -27.75. The sequence is geometric, with the first term a1 = 5 and common ratio = 4 an = an-1 + 10 Domain: All real numbers \(\frac{1}{16}\)1/4 On the first day, the prices of the sweaters are reduced by 20%. The amplitude numbers are neater and a little easier Answer: d. Volume = 3.375 m The formula for the volume of a regular dodecahedron is V 7.663, where is the length of an edge. (5/2)^7-1 PROBLEM SOLVING 78.5/80.5 = 0.975 \(\frac{3}{49}\), \(\frac{3}{7}\), 3, 21, . V = s USING PROPERTIES y = 2(9)0 = 2(1) = 2 A magnitude earthquake is times bigger than a magnitude earthquake, but it is times stronger (energy release). 5^(n-1), Question 8. Answer: The graph shows the balance of a savings account over time. Write a function of the form y = abx that represents a real-life population. 216 = s r = 0.12 y = a(1 r)t (b) 0 < a < 1. s(t) = 0.65(0.48)t . a6 = -32 -2 = 64 When bases are equal powers should be equated. Graph f(x) = 2(6)x. Answer: How to Use Greater Than Less Than Calculator? = (y4/3)3 / 2 -12 + 2 = 4x 3x Write a function that represents the number of people who have received the email after n days. If both the numbers are equal, we use an equal sign. Answer: 0.1, 1, 10, 100, . So, the next three terms are 4, 0.8, 0.16, Question 6. a3 = -27 \(\frac{4^{-3} a^{0}}{b^{-7}}\) You can improve your subject knowledge by taking the help of the BIM Algebra 1 Solution Key and stand out from the crowd. i like this but its a little bit boring but it helps. Write your answer using only positive exponents. r = 1 \(\frac{4}{5}\) The index n = 9 is odd = 13 + 8 = 306, Question 3. 5 = n . a3 = 9 + 5 = 14 b. a4 = 20 a4 = \(\frac{1}{4}\)a3 1= \(\frac{1}{4}\)(2) = 1/2 a4 = 16/4 = 4 y = 1.5(2)0 = 1.5(1) = 1.5 Question 46. = 64, Answer: Answer: Question 36. y = 2(9)x After the second round, 32 teams remain. Answer: Question 30. d = a2 a1 The domain of -(0.5)^(x 1) is all real numbers whereas range of -(0.5)^(x 1) is y < -1 Evaluate the function when t = 3. Use properties of exponents to find the value of r. a. a3 is negative times the second term MODELING WITH MATHEMATICS Answer: 1.3, 2.6, 3.9, 5.2, 6.5, . Answer: . a2 = 8 (1/2)^(n-1). Answer: Question 69. . Answer: 1. Essential Question Answer: Question 12. Question 22. 6, 3, 0, -3, . r = -12/-2 = 6 Explanation: 22x = 26 (\(\frac{1}{3}\))2x + 3 = 5 Question 14. h(t) = 1250(0.135) y = 2(9)-2 = 2\(\sqrt[2]{9}\) = 2(3) = 6 Given Question 65. 13, 26, 52, 104, . In Exercises 1924, write the next three terms of the geometric sequence. b = 2 ft When comparing decimals, it's always important to line up the digits correctly so you can properly interpret which one is bigger. This portion of the guide explains how to find the Rick and Morty Easter Egg and potentially get a legendary gun out of it. a2 = -18 How many times larger is 900 than 9? In each table, what do you notice about the values of x? a2 = 8 5 = 40 6x 3y 12, Question 5. FV = 750(1.0125)4t, Question 19. The common difference is 11. an = 13 . To compare two decimals, we should start by looking at the largest place value. a1 = -1 Question 12. b. Rewrite each fraction from part (a) in the form 2x. Each term of the sequence is 10 more than the preceding term. Answer: a6 = 4 243 r = 0.52 y 6 = 3x 6 Write your answer using only positive exponents. Write the next three terms of the geometric sequence. The cookie is set by GDPR cookie consent to record the user consent for the cookies in the category "Functional". Direct link to Serena Cole's post who is the creator of kah, Posted 21 days ago. . Question 7. I really liked how the chat box was here before and I kind of miss having it so I wish BYJUS would bring it back but everything besides that I love and I am so excited to be learning with the learning program team! = 27. How many times does Pluto orbit the Sun while the Sun completes one orbit around the center of the Milky Way? (\(\frac{6 c}{7}\))-2 y 800(0.71)t HOW DO YOU SEE IT? 53x+8= 52x 3(2x + 2)3 = 3(x + 4)4 (5)(55) = 125 3125 = 390625 3x = 243 i. . a1 = 16, an = 0.5an 1 . answer choices 1,000 times 1 time 10 times 100 times Question 4 30 seconds Q. Write an equation for g. What is the hardest concept in chemistry? Your Mobile number and Email id will not be published. f(t) = 5(1 + 3)t r = 3 i. f(x) = 3x 2 A magnitude 8.7 earthquake is 794 y = 1.5(2)x t number of decay periods. (Section 3.3), Question 58. One of the smallest plant seeds comes from an orchid, and one of the largest plant seeds comes from a double coconut palm. = 45 The recursive rule represents a geometric sequence. Answer: Question 48. an+1 = an 14Tn = a + (n 1)d 2x 4 = x a1 = -2, an = 9an 1 Consider a hypothetical population of rabbits. (b) Find the approximate monthly percent decrease in value. The greater than symbol is generally remembered using the alligator method. d. y = (\(\frac{1}{2}\))x 1 + r > 1 g(x) = 8x + 16 8x 2x = -2 + 8 D MATHEMATICAL CONNECTIONS COMPARING FUNCTIONS The graphs of f and g are shown. The table shows the value of a camper t years after it is purchased. Answer: After how many clicks on the zoom-out button is the side length of the map 2560 miles? (6.1 10-3)(8 109) It takes the Sun about 2.3 108 years to orbit the center of the Milky Way. 24x = 2x + 9 f(x) = -2x + 4 f(x) = 0.5x; x = -3 The volume of a cube-shaped box is 275 cubic millimeters. So, the arithmetic sequence is 2. (\(\frac{1}{3}\))x 1 =3 When bases are equal powers should be equated. Describe the information given by each of the functions. PROBLEM SOLVING The magnitude scale is really measuring the physical size of the earthquake, y = (1 0.09)t Then enter =A1+2 into cell A2, as shown. a4 = 16 y = 50(2)1 2d 7 8d r = 1.05 1 Write a function whose graph is a horizontal translation of the graph of h(x) = 4x. a25 = 0.01(2)^24 y = 10(1 + 0.4)5 There is no common difference. . 8, 3, -2, -7, -12, . Answer: Question 27. Student A claims he can form a linear system from the equations shown that has infinitely many solutions. Work with a partner. What is scientific notation? Chemistry, generally speaking, is the study of matter and how matter changes. Question 49. Write and graph an exponential function f represented by the table. . 3. Question 67. So for the first number, 5, 462. We also use third-party cookies that help us analyze and understand how you use this website. Answer: Answer: Question 28. An expansion of the alimentary canal that lies immediately inferior to By the end of this section, you will: Explain how various factors contributed to the American victory in the Revolution If the Patriots were to be successful in their fight against the British, Vekke Sind is reader-supported. After how many weeks will the stock be worth $20? Answer: Question 56. r = 1 0.48 p(t) = 1.85 2 2 2 2 2 x = \(\frac{1}{2}\) y 6 = m(x 2) 2x x = 1 Explain your reasoning. 4, 20, 100, 500, 2500, . Compare the account balances. Answer: do I know immediately that's the larger number? d. Is it possible for an exponential equation to have no solution? In Exercises 3538, graph the first four terms of the sequence with the given description. Play this game to review Other. In Exercises 5962, rewrite the expression as a power of a product. Write a recursive rule and an explicit rule for the sequence. = 3 30 t = 5 Question 1. The domain of a function is the set of all values for the function is defined. As the independent variable x changes by a constant amount, the dependent variable y is multiplied by a constant factor. 3/2x + 4 = 10 a5 = 1000 5 = 5000 In a more formal sense, chemistry is traditionally divided into five major subdisciplines: organic chemistry, biochemistry, inorganic chemistry, analytical chemistry, and physical chemistry. What Happens: You incorrectly read or do not understand directions. Does the function represent exponential growth or exponential decay? So no matter how you think says log(E) is proportional to 1.5M, where E is energy and M is magnitude. a5 = -18 a. Cite. ., -8, 0, Thank you very much for your cooperation. a. y = 2x Answer: \(\sqrt{64}\) = \(\sqrt{8}\) = 8, Question 5. (\(\frac{1}{64}\))1 / 6 1/2x = 16 . 16 can be written as 24 2-x + 1 = \(\frac{3}{4}\)x + 3 Australia. a1 = -192 x 3 = log 200000 log (192)/log (4) z-2+4= z, Question 5. 10 6 = 4 The sequence is geometric. d = -13 Check your solution. a1 = 4 2x 2 = \(\frac{3}{2}\)x 2. The table represents an exponential growth. ones place, they seem comparable to each other. So, a magnitude 8.7 2x 3x = -1 4 r = ak+1/ak So here, once again, you're If so, find the common difference. b. . 3x = x + 10 n 1 = 5.989 r = 3.5% or 0.035 EXPLORATION 1 b. Graph the functions from part (a) in the same coordinate plane. As x increases by 1, y is multiplied by 1/11. Question 55. 1 r = 1.1 r = 0.11 Answer: P = 300 Answer: The graph is asymptotic to the x-axis as x approaches negative infinity. b. a2 = -4a2 1 = -4(-7) = 28 an = -n + 1 What place is the 4 in the number 34,865? The result is the number of times the first number is Answer: Question 18. a present value . y = 15 3 = \(\sqrt[3]{125}\) y = 53.7 a1 = -375 Show that when x is increased by a constant k, the quotient \(\frac{f(x+k)}{f(x)}\) is always the same regardless of the value of x. 205/128 1.6 . The green curve y = 2^x does not have a solution Its value decreases by 14% each year. x = 8 f(1) = -1, f(n) = 6f(n 1) a5 = 375 (-5)4 = 234375 a1 = -45, an = an 1 + 20 y3 y-5 b. an = a1 rn-1 The sequence is neither arithmetic nor geometric sequence because it does not have any common difference. Answer: = 1.1 14641 Do not attempt to solve the equation. can yall give us hints that still give us credit bc mine keep sayin that I cant get credit and this suff is confusing, I am a professional at decimals now thanks to your videos. a. I would certainly used this again and I would recommend this to my friends. Approximate the number of visitors after 5 months. Question 63. 0.6, -3, 15, -75, . (4/3) = (64/27) The sequence is a1, a2, a3, a4, a5. So, the table represents exponential decay. At sea level, Earths atmosphere exerts a pressure of 1 atmosphere. = 3 + 2(-15) Answer: Question 18. an = -4n + 2 a4 = -10 (2)4 = 28 It takes Pluto about 2.5 102 years to orbit the Sun. 2x = \(\frac{1}{2}\) Work with a partner. y = 4681 grills in 6 years. Answer: Answer: Question 48. The mass of Jupiter is 1.900 * 1027 kg and the mass of the moon is 7.350 * 1022 kg. (c) Does this bacterial population grow faster than the bacterial population in Example 7? Graph the first four terms of the sequence. Domain: All real numbers (See Example 1.). The given statement is wrong. b = 1 + r . a3 = -12 Answer: Question 71. Question 53. . 52y8/22x4 Explain your reasoning. Is your friend correct? In 2016 = 7 + 11 Functional cookies help to perform certain functionalities like sharing the content of the website on social media platforms, collect feedbacks, and other third-party features. y = 135 coyotes. form a geometric sequence? . y = 14.76(1.4)t . . = (3) 2. The sequence is arithmetic. Given, 5462 = 5000 + 400 + 60 + 2 and 2341 = 2000 + 300 + 40 + 1, so that's another way to look at it. NUMBER SENSE During a flu epidemic, the number of sick people triples every week. a7 = 832, Question 10. Explain your reasoning. a6 = 768 4 c. The population growth rate is more than the bacterial population in Example 7. c. You zoom in twice. an = r . Answer: -2, -12, -72, -432 \(\sqrt[3]{8}\) = 81/3 It is estimated, that in 1782, there were about 100,000 nesting pairs of bald eagles in the United States. . Find a formula (for instance, from geometry or physics) that contains a radical. a = 500 (c) Graph the function from part (a). 92x = 3x 6 What fraction of the original piece of paper is each shaded part? a6 = -3/4 -1/4 = 3/16 Answer: Question 66. Describe the domain and range. Domain: [0, 8]. The function represents exponential growth. \(\sqrt[5]{34}\) t = t/12 This cookie is set by GDPR Cookie Consent plugin. Hi! Given, Thus the volume of the cedar chest is 48 cu. Student C claims he can form a linear system from the equations shown that has no solution. y = 8 0.614 Explain. Question 19. The table represents an exponential growth function. Thus the percentage of temperature drop will be 2.5%. Many found the CBSE 12th Term 2 Chemistry paper to be tricky. Although a minimal amount of carbohydrate digestion occurs in the mouth, chemical digestion really gets underway in the stomach. Is your friend correct? Determine whether the function represents exponential growth or exponential decay. In Exercises 914, determine whether the sequence is arithmetic, geometric, or neither. 80.5/0.975 = 82.6 192, 24, 3, \(\frac{3}{8}\), , . The first term of a sequence is 16. Students can answer the questions in either part with agree or disagree. In this context, it basically means "makes me think" or "gives me the impression". (c) Graph the function from part (a). Answer: Question 42. In Exercises 4956, rewrite the function to determine whether it represents exponential growth or exponential decay. y6/y5 = 1.43 Answer: 216 = 6^(n-1) Answer: 5x + 12x Explain. Answer: Question 11. a2 = 48 Answer: In order to define a sequence recursively, we must state the first term and then state a rule for how each successive term can be described from the one before it. an = a1 . cannot be represented by a recursive rule. Use a graphing calculator to graph the function. Answer: Question 20. 2x 7 = 24/12 f(x) = 3(2)^-1 . an = 3 . =\(\sqrt[4]{1/16}\) = 1/4, Answer: Explanation: \(\frac{2^{-2} m^{-3}}{n^{0}}\) DRAWING CONCLUSIONS A college student makes a deal with her parents to live at home instead of living on campus. Apply log on both sides t(46) = 16105.1 a7 = 432(1/6)^6 = (3)5 The number 900 is 10 times larger than 90. \(\sqrt[4]{16}\) = -2, Question 2. b. -8 (-5) = -8 + 5 = -3 x = -4, Answer: Fill in the exponent of x with a number to simplify the expression. Answer: The equation y = -6x does not represent an exponential function because it does not fit the pattern y = ab^x. In Exercises 21 and 22, rewrite the expression in radical form. So if you subtract the smaller value from the larger value, you will find the difference, or how many more one quantity has than another. x = 8 + 4 (a) a > 1 and Given, Answer: (\(-\frac{4}{n}\))5 How many times larger than 90 is 900? Rewrite the problem using the same base. a4 = 2 Write a sequence in which each term an is the side length of square n. Answer: number of thousandths. y = 50(1.11) How many people will have visited the website after it is online 47 days? d = 4 (-1) = 5 y = 8(0.85) Answer: Question 14. Answer: r = 2 The cookie is used to store the user consent for the cookies in the category "Performance". r = 0/8 = 0 y = \(\frac{1}{4}\)(4)x; x = \(\frac{3}{2}\) a2 = 3 Answer: Core Concepts From the graph, the domain is all real numbers and the range is y > 0. c. What is the yearly percent change? y = 42,500(1 + 3%) In order to continue enjoying our site, we ask that you confirm your identity as a human. Question 53. 2x = -4 Question 9. 32, 8, 2, \(\frac{1}{2}\), . a5 = 72.9 9 = 656.1 Its value decreases by 14% each year. Answer: rewrite the formula using rational exponents Check your solution. a6 = a5 r Answer: a1 = 1 In Exercises 1318, evaluate the expression. = -8 \(\frac{1}{125}\) c-12. 34x + 3 = 81x Answer: B an = 8n 12. Identify the percent rate of change. Answer: = \(\sqrt[4]{256}\)5 Question 7. -6x 6x = 48 P = 300 34x 9 = \(\frac{1}{3^5}\) Given, Explain your reasoning. The range of a function is a set of solutions to the function for a given input. y = 200^x And here, you have 8/1000. = x5/3-1+1/3/x-2 = x1+2 = x, Question 2. since 1 unit of magnitude is 10 times the amplitude on a seismogram and 0.1 1, 1, 0, -1, -1, 0, 1, 1, . Try BYJUS free classes today!Right on! a2 = 54 r = \(\frac{5}{5}\) \(\frac{4}{5}\) MAKING AN ARGUMENT The words "greater" and "larger" are exact synonyms! Describing a Pattern Geometric sequence an = a1 . Answer: The first term of a sequence is 19. 2-2h, Question 16. \(\frac{3}{49}\), \(\frac{3}{7}\), 3, 21, . Answer: Question 16. f(x) = 10 3x 2x = -4 Graph g when g(0) = 4. a1 = 1 How many digits does the number after 99 have? \(\sqrt[3]{-125}\) Question 43. Your friend says that the sequence is not geometric. Then find a6. a2 = -1(6)^1 = -1 6 = -6 s = \(\sqrt[3]{V}\) \(\frac{x^{5}}{x^{4}}\) x How can you write and evaluate an nth root of a number? \(\sqrt[3]{-125}\) a4 = -3 s = 1.5 m, e. Volume = 1 yd Question 17. 2x = 2 a1 = 4, an = an 1 + 5 Question 27. . a = 475 Find both answers. b. . r = 15/-3 = -5 Can water stay liquid below zero degrees Celsius? Answer: a1 = -6 a1 = 8, an = an 1 12 . The population of a city has been increasing by 2% annually. 13500 8500 = $5000 r = 9.22. The fourth root of 16 is 2 Question 19. c. Do you agree with the statement below? y = 500(1 + 0.75%)12t, Question 9. 9, -18, 27, -36, . Equality and inequality symbols are used to compare two values. an = 486 (3)8 = 486 6561 = 3188646. So this number on the left The function is of the form y = a(1 + r)t (2)(2) = 2 2 2 2 2 = 32 Question 23. WHICH ONE DOESNT BELONG? Allot time to the areas you feel difficulty and solve accordingly. . Graph the function. t(47) = 1.1 t(46) (-3, 0) The function is of the form y = a(1 r)t What are some of the characteristics of the graph of an exponential function? Question 3. On day 1, you run 1 km. Here x is increased by 1, y is multiplied by a factor of 3. Given, Answer: The sign shown is from the year 2000. WHICH ONE DOESNT BELONG? The value of the function at 0 is 5. 2/16 = 1/2 You deposit $500 in a savings account that earns 9% annual interest compounded monthly. b. Answer: a3 = 9 \(\frac{5^{-1}}{-9^{0}}\) . What are the 3 main branches of chemistry? r = 32/64 (\(\sqrt[3]{512}\)) = -4, Question 18. After you zoom out a second time, the area is 1536 square units. 0.1, 1, 10, 100, . Given Answer: Question 42. Answer: Question 36. a5 = -4a5 1 = -4(448) = -1792 f(t) = 0.4/1.16 (1.16)t I'll help you understand math! Other uncategorized cookies are those that are being analyzed and have not been classified into a category as yet. USING TOOLS You can use a spreadsheet to generate the terms of a sequence. an = (1.2)^(n-1) Answer: b. s = \(\sqrt[3]{125/8}\) a25 = 167772.16 Given, a3 = 2 Answer: Question 18. The sequence does not have a common difference. y = 5(1.08)t a3 = 1.5a3 1 = 1.5(12) = 18 Answer: d. 3x = 9 y = 16(2) = 16(1) = 16 . Answer: There is no common ratio. 4/2 = 2 y = \(\frac{1}{4}\) 8 PROBLEM SOLVING The first point is (1, 64) (2)^7-1 Question 25. Describe the effect of a on the graph of y = a 2x when a is positive and when a is negative. a. Graph the function. = t 12 months Given, Answer: Solve the equation. Answer: USING STRUCTURE Question 8. How can you solve an exponential equation graphically? x = -4. Explain your reasoning. Question 35. r = 0.18 s = \(\sqrt[3]{3375}\) Question 14. Answer: Question 58. Compare the results with the sequence of the number of pairs in Exploration 1. ERROR ANALYSIS The growth rate of a bacterial culture is 150% each hour. d. Part (a) involves a geometric sequence with a common ratio of 2. Answer: a1 = -4 The cookies is used to store the user consent for the cookies in the category "Necessary". How did you decide on an appropriate level of precision for your answer in Exercise 49 on page 330? And here-- let me do that Answer: Answer: a. Answer: Exponential Functions and Sequences Chapter of Big Ideas Math Algebra 1 Answers provided helps students to learn the fundamentals associated with Exponential Functions and Sequences. you get 900/1000. = 3435 x = 4 1/2 Answer: incrementing the thousandths here, you go from Work with a partner. Question 47. (\(\frac{1}{3}\))2x (\(\frac{1}{3}\)) = 5 Given, r = 11/100 The first, titled Arturo Xuncax, is set in an Indian village in Guatemala. Describing a Decay Pattern V = 1/6(1.77)S3 / 2 Question 4. f(2) = 6, f(-1) = -3 Texas and Mexico share 1,254 miles of common border and are joined by 28 international bridges and border crossings. PROBLEM SOLVING 34x 9 = 3-5 Answer: r = 12/-3 Greater Than Less Than Calculator is a free online tool that displays the result whether the first number is less than or greater than the second number. . an = a1. Given, . Round your answer to the nearest thousand. Given, a1 = 10 The sequence has no common ratio y = 1.5(2)x So, the common ratio is -1/3. (-81)3 / 4 = (\(\sqrt[4]{-81}\)) The graph is a linear function. Describe the pattern. (r)^(n-1) r = 3 The population is expected to increase by 5.5% annually for the next decade. 4/100 = 0.04, Question 66. a3 = 16 \(\frac{y^{6}}{y^{7}}\) (-25)1 / 2 Then find the cube root. . \(\sqrt[6]{20000}\) = 5.21, Question 3. 256 can be written in the fourth root as 44 Explanation: 328/205 = 1.6 However, if you consider that 2 is one time greater than 1, then it would follow that 5x greater would mean a total of 6x as great. ii. a2 = 4 + 5 = 9 Plot the points (0, 100) and (1, 200). Question 32. (\(\sqrt[5]{7}\))x = 52x + 3 a3 b3 = 18 25 = -7 Given, In Exercises 35 and 36, describe and correct the error in simplifying the expression. Question 8. Which among the below is not a city? The sequence is neither geometric nor arithmetic. 7x 4 = 78 Given, Atmospheric pressure P (in atmospheres) decreases with altitude. a2 = -75 The function represents a geometric sequence MODELING WITH MATHEMATICS The distance (in millimeters) traveled by a swinging pendulum decreases after each swing, as shown in the table. (a) Write an exponential growth function that represents the website membership t years after 2010. Answer: WRITING 2x + 4 = 3x 1 Answer: Question 22. Given, = 8 = 1280 Characteristics of the exponential function is #2. times bigger mean in math? Your school is conducting a survey. MATHEMATICAL CONNECTIONS In Exercises 39 and 40, (a) write a function that represents the sequence of figures and (b) describe the 10th figure in the sequence. a1 + a2 = 2 The exponential function y = V(x) represents the projected value of a stock x weeks after a corporation loses an important legal battle. Answer: The 8 in 800 is 10 times more than the 8 in 80. Not sure which number is the larger one. In Exercises 510, determine whether the equation represents an exponential function. What is the greatest number of times you can fold a piece of paper in half? Interest rates, depreciation, and inflation are all factors. Answer: Question 57. a1 = 32, an = \(\frac{1}{4}\)an 1 So, the 6th term is 5904.9. . . 4x x = 9 -4 216 = 64x r = 4/1 = 4 A bacterial population doubles each hour. Answer: Question 40. 6^(n-1) a6 = a5 + a4 What is the value of the camper after 5 years? VOCABULARY x = 2 after 40 years . In the same viewing window, graph a linear equation (if possible) that does not intersect the graph of y = 2x. The explicit rule represents an arithmetic sequence a. Answer: Question 65. Therefore, using the y = 10(1 + 0.4)t a1 = 1 Answer: r = a2/a1 Question 44. . The parent function is g(x) = (\(\frac{1}{3}\))x. Question 1. On what day do you run approximately 3 kilometers? the numerator and denominator by 10-- plus 8/1000. How many times bigger is the volume of pyramid B than pyramid A? Answer: y = (-3)^x does not belong with the other three because the range of y < 0. Hello Latrice, The value of 123. \(\frac{1}{128}\) = 25x + 3 r(t) = (0.88)4r This was realy very useful. h. 3x + 2 = \(\frac{1}{9}\) \(\sqrt[4]{16}\) i. . a2 = 26 Once the bases are the same, drop the bases and set the exponents equal to each other. So, the 6th term is 7. 122x-1 = 12x/4 Answer: Question 35. Given, \(\frac{x^{4}}{x^{7}}\) = x4-7 = x-3, Question 4. You continue to increase its size repeatedly by 100% using the computer. Some of the inequality symbols are less than, Frequently Asked Questions on Greater than Less Than. 10, 20, 30, 40, . The cookie is used to store the user consent for the cookies in the category "Analytics". y = 0.1(1.23)t (\(\frac{1}{2 k^{2}}\))5 Similarly, How many times larger is 100 than 10? Question 3. 27x = 9x 2 25/2 = 2 = 8 y = 6(2)x 4 1 a3 = a3-1 + a3-2 an = an-1 r. Explain your reasoning. How do you score a 90+ class 12 in chemistry? r = 0.12246 In Exercises 2530, graph the function. WHICH ONE DOESNT BELONG? = 32, Graph the function. . When I learned this many years ago, I remembered I was taught that 3 times bigger than is the same meaning with 3 times as big as. Initial amount = 1 Question 14. = a3 + a2 6. So far, out of the two digits, Question 8. Question 13. \(\sqrt[3]{3}\) = 3, Answer: a2 = -3 a. an = 20(4/3)^(n-1) matches with graph B. r = 11/4 = 2.75 Answer: Question 50. 4% How can you solve an exponential equation graphically? . r = 0.05 an = a(n-1) + 8. (\(\frac{1}{27}\))4-x = 92x-1 The change in x-values is Use a calculator to approximate the circumference of its femur. 5. Answer: MAKING AN ARGUMENT You are given two consecutive terms of a sequence. Range: y > 0, Answer: 5 1 = 4 r = a2/a1 = -5/1 = -5 1. Answer: Question 34. What was created to prevent similar banking disasters? This is an amazing website and has really helped me with my mathematics homework!!! Below well explore proven strategies and techniques that will, if applied, improve your ability to study and learn chemistry. Question 26. There is so much more to buying a new car than the purchase price. Answer: And so what is this Essential Question a. When bases are equal powers should be equated. 3% b. not the STRENGTH (energy) of the quakes. Volume = 125 cm3 Each term of the sequence is 5 times the preceding term. Question 12. 1, 4, 16, 64, . 64 = 4 In Exercises 43 and 44, graph the function with the given description. Answer: How thick is the result? Answer: The second term of a sequence is 7. n = 3, a = -125 Justify each step in showing that a recursive equation for the sequence is an = an 1 + d. 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