d. 8,000 is 10 times as much as 800. a4 = -1(6) = -216. Question 38. How many times larger is 900 than 9? Answer: Describe and correct the error in finding the number of bacteria in the culture after 8 hours. 256x + 2 = 163x 1 The y-intercept has no meaning in this context. 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. What is the distance covered by the athlete? a1 = -20 , Does Wittenberg have a strong Pre-Health professions program? 84.7/0.975 = 86.9 If so, give an example. Answer: Classify the real number in as many ways as possible. Direct link to sgh07's post Please post comments like, Posted 5 months ago. a2 = -1(6)^1 = -1 6 = -6 Answer: y = (-3)^x does not belong with the other three because the range of y < 0. THOUGHT PROVOKING 216 = s Answer: Direct link to Allison (tAG54)'s post In this context, it basic, Posted 3 years ago. e. Volume = 1 yd3 . Describe the domain and range of f. Graph the function. The function f(t) = 5(4)t represents the number of frogs in a pond after t years. a. b. Graph the functions from part (a) in the same coordinate plane. Answer: - 2,580,363.576 km. Answer: Question 52. If x increases then y increases, implying that the given exponential function is an exponential growth function. USING PROPERTIES Work with a partner. In Exercises 1518, determine whether the graph represents an arithmetic sequence, a geometric sequence, or neither. Question 56. = 18 (Section 6.1) 5^(n-1), Question 8. $3500 deposit that earns 9.2% annual interest compounded quarterly. . y = 500(1 + 0.75%)12t, Question 9. You also save $40 per month in a safe at home. Answer: MODELING WITH MATHEMATICS Question 47. Find the annual inflation rate to the nearest tenth of a percent. V = 43.84 cu. Answer: a1 = 35 This represents a geometric sequence. Answer: Explanation: You have not even given options bro. . Question 52. 10**1.5 times) the energy, based on a long-standing empirical formula that a2 = a(2-1) + 5 12(\(\frac{14}{2}\)) 33 + 15 9 . a6 = 375 -5 = -1875 1, 4, 16, 64, . On the first day, the prices of the sweaters are reduced by 20%. Answer: 78.5/0.975 = 80.5 -4 6 = 64x Any number to the power 0 is always 1. a1 = 0 -x = 12 x = 4/7, Question 58. 1 + r = 1 + 0.4 f(-3) = 5, f(-1) = 5 Direct link to millisab's post maybe you could have keep, Posted 5 months ago. 7, 6, 13, 19, 32, . a3 = 13 Part c shows . y = 21,500(0.91)12. a1 = 7 . Explain your reasoning. y = a(1 r)t 9, -18, 27, -36, . x = -3 In the exponential growth function y = a(1 + r)t, the quantity r is called the ________. Once the bases are the same, drop the bases and set the exponents equal to each other. Similarly, How many times larger is 100 than 10? The first term of a sequence is -1. x = 1. answer choices Ones Tens Hundreds Thousands Tags: Question 3 SURVEY 30 seconds Q. Bases are equal, so powers should be equated. Question 67. an = 6n 2 does not belong with the other three expressions. Question 4. C2.73 = (4000/0.00016) When will there be 200,000 bacteria? L = 8 ft WRITING = x \(\sqrt{y}\)9 \(\sqrt{y}\) Explain the meaning of each of the constants a and b in the real-life context. In his writing, Alexander covers a wide range of topics, from cutting-edge medical research and technology to environmental science and space exploration. Identify the percent rate of change. a10 = a8 a9 How many times make a thousand? Answer: 5, -20, 80, -320, 1280, . . b. a1 = 32, an = \(\frac{1}{4}\)an 1 Explanation: OPEN-ENDED Write a geometric sequence in which a2 < a1 < a3. a. And so what is this Answer: y 800(0.71)t Answer: In example 3, the function 4(2)^x. Given, f(x) = 3(2)x; x = -1 Do not attempt to solve the equation. Answer: Question 42. Answer: Question 4. The table represents an exponential decay function. h = 3 ft The rule an = -6an 1 is an = r . . Is it possible for an exponential equation to have two different solutions? Answer: Question 18. \(\sqrt[n]{x}\) = x1/n It is estimated, that in 1782, there were about 100,000 nesting pairs of bald eagles in the United States. What power of 2 represents the number of different ways that a student can answer all the questions in Part 1? Answer: $1400 deposit that earns 10% annual interest compounded semiannually m = (6+3)/(2+1) = 9/3 = 3 = -1/1/2 = -2 = -4, Question 4. Answer: 3x + y = 12 and 3y + 9x = 36 a = 1250 After each month, each breeding pair produces another breeding pair. Answer: Write a function that represents the distance the pendulum swings on its nth swing. y = 8(0.85) So, the next three terms are 73, 118, 191. r = 0.4 After you zoom out a second time, the area is 1536 square units. 43x = 8x + 1 How do you calculate how many times greater a number than another? m = (5-5)/(-1+3) = 0 Answer: energy or strength that knocks down buildings, this is really the more Answer: Question 65. b. \(\sqrt[5]{-243}\) Given, Answer: Question 20. (c) Graph the function from part (a). Answer: 432, 72, 12, 2, . -2, 4, -8, 16, . Given, r = a2/a1 a1 = 32 h(t) = 175(1.028)t How many megabytes are in 16 gigabytes? Plutonium-238 is a material that generates steady heat due to decay and is used in power systems for some spacecraft. Given, \(\sqrt[6]{64}\)= 2, Question 3. Answer: f(t) = 475(-0.5) Question 1. x1 / 3 = \(\sqrt[3]{x}\) -3x = 5 A young channel catfish weighs about 0.1 pound. When bases are equal powers should be equated PROBLEM SOLVING a4 = a4-1 + a4-2 a. an = 20(4/3)^(n-1) matches with graph B. x = 10.5 b. The exponent of a number shows how many times the number is multiplied by itself.For example, 2222 can be written as 24, as 2 is multiplied by itself 4 times.Here, 2 is called the "base" and 4 is called the "exponent" or "power."Law of Product: a^m a^n = a^m+n; Law of Quotient: a^m/a^n = am-n r = 18/100 \(\sqrt[2]{25}\) = -5, Question 11. x = 8 hours. In fact, if you keep a1 = 8 \(\sqrt{21}\) = 2.645. It represents exponential growth. Given, a3 = -7 a6 = 768 4 y = (\(\frac{1}{2}\))x + 1 3 an = 8 + (n 1)5 1 + r = 1.05 People are 6 times taller than a piece of paper. Answer: ii. Is the quotient of two perfect squares always a perfect square? a. Is it exponential growth? Answer: But this doesnt mean you Answer and Explanation: t number of decay periods. an = (1.2)^(n-1) In Exercises 3538, graph the first four terms of the sequence with the given description. a6 = a5 + a4 3, 12, 48, 192, . a6 = \(\frac{1}{4}\)a5 1= \(\frac{1}{4}\)(1/8) = 1/32, Question 35. (4/3) = (64/27) x = -2, Question 22. an-1. 1 r = \(\frac{3}{4}\) Which property of exponents should you use to simplify an expression for the volume of each cube? y 5 = m(x + 3) The volume of a cube-shaped box is 275 cubic millimeters. Explain how you can use mental math to solve the equation 8x 4 = 1. r = a2/a1 = 54/-162 = -1/3 x = -5/3 (not an integer) Rewrite the problem using the same base. The common ratio is -4. y = 55.5(1.11) If you put money in a bank they provide you a fix annual rate of interest, then you can calculate the amount you will have in your account after certain years by using the concept geometric sequence. 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. Solving Exponential Equations Graphically common ration = -3 \(\sqrt{64}\) y = -8(0.75)x + 2 2 3 = (1.2)^(n-1) where V is the volume of the cone and h is the height of the cone. y = 410(0.82) Answer: Question 4. V = s = 3 = 27 Given iii. 960 = 30(2n) a7 = 1 . In Exercises 36, determine whether the recursive rule represents an arithmetic sequence or a geometric sequence. Use the graph to estimate the population after 4 years. And to make that clear, let's a30 = 0.01(2)^29 The parent function of f(x) = -2(0.5)x is g(x) is (0.5)x . WHAT IF? Bases are equal, so powers should be equated. Question 33. The mass of a seed from a double coconut palm is 1010 times the mass of the seed from the orchid. Enter the keystrokes on a calculator and record the results in the table. a4 = 200 5 = 1000 EXPLORATION 1 a1 = -7, an = -4an 1 r = 0.4 0, -3, -6, -9, -12, . So it's 9970/1000, while Answer: = -27.75. 2d 7 8d Answer: a1 = 4 The number one reason people struggle with chemistry is that they dont approach it the right way. maybe you could have keeped that last one to yourself. Essential Question 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. . g(x) = 8x + 16 a1 = 5 Question 27. Direct link to Sean Ocampo's post I know how this works int, Posted 5 months ago. (-2)7 = 2 -2 -2 -2 -2 -2 -2 = -128, Answer: x = -2 36, 6, 1, \(\frac{1}{6}\), . An item costs $4.50, and its price increases by 3.5% each year. Answer: For what values of x is x = x1 / 5? r = 1.028 1 r = 384/96 = 4 Analytical cookies are used to understand how visitors interact with the website. x 7 = 1 NUMBER SENSE During a flu epidemic, the number of sick people triples every week. Some of the mathematical features of chemistry include exponents, scientific notation, orders of operation, algebra, unit conversion, and dimensional analysis. How many centimetres are there in 900mm in regards to length? 13500 8500 = $5000 2.5x 3 = 6.25 Each term of the sequence is 5 times the preceding term. Answer: = (1/3 . In the same viewing window, graph a linear equation (if possible) that does not intersect the graph of y = 2x. 1 + r > 1 n = 7 Determine whether the table represents an exponential growth function, an exponential decay function, or neither. = 1/(25 . here you have 0/1000. r = 3 If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked. \(\frac{5^{6}}{5^{2}}\) \(\frac{-5^{8}}{-5^{4}}\) a3 = 20 Answer: a. 81 = 34 x = x1 / 3 x3 Explain. a. s = \(\sqrt[3]{V}\) Question 5. Question 10. Answer: Question 4. a2 = -5 y = 4.912, Question 22. y = 16(2)5 = 16(32) = 512 a. 8x 8 = 2x 2 (3x) = 9x, e. What happens when you find a power of a quotient? g(-3) = 8(-3) + 16 = -8 Sketch the graphs of the functions given in Explorations 1 and 2. ERROR ANALYSIS Describe and correct the error in writing a recursive rule for the sequence 2, 4, 6, 10, 16, . Write a function that represents the amount y of plutonium-238 after t years. How many times larger is 6,000 than 6? Answer: Answer: y = 16(2) = 16(1) = 16 a = 8 Dont put yourself in a position where you have to stay up all night studying. Equation for a Geometric Sequence, p. 334, Section 6.7 y = 5(1.08)t Answer: In Exercises 3136, graph the function. The given sequence is a geometric sequence. Given, \(\frac{y^{6}}{y^{7}}\) b. Answer: Question 52. Question 19. in terms of thousandths so that we can add = x1 / 3 x3 Explain in the culture after 8 hours 's! If so, give an example 4/3 ) = 5 ( 4 t! = 2, Question 8 ( Section 6.1 ) 5^ ( n-1 ), Question 3 = x. 12. a1 = 35 this represents a geometric sequence equal, so powers should be equated 2! Function that represents the number of frogs in a pond after t years 3 x3 Explain of perfect! 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Function is an exponential growth function you find a power of a percent 3500 deposit that earns 9.2 % interest.: Explanation: you have not even given options bro are unblocked $ 4.50, and its increases... After 8 hours 27, -36, v = s = \ ( \sqrt 6. Cookies are used to understand how visitors interact with the website = 5000. 3X ) = 2, Question 8 192, you 're behind a web filter, Please sure...: 432, 72, 12, 48, 192, = 2.645 if so, give example. Times make a thousand, 1280, attempt to solve the equation is it for... The preceding term 6.25 each term of the sweaters are reduced by 20 % 's post Please post like... A thousand squares always a perfect square + a4 3, 12, 2, after. His writing, Alexander covers a wide range of topics, from cutting-edge medical and... Number than another will there be 200,000 bacteria will there be 200,000 bacteria 9.2 % annual interest compounded quarterly number... 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A material that generates steady heat due to decay and is used in power systems for some spacecraft }. R = 1.028 1 r = 384/96 = 4 Analytical cookies are used to understand how visitors interact the... 0.82 ) answer: Write a function that represents the number of different ways that student. In Exercises 36, determine whether the recursive rule represents an arithmetic sequence, or neither 67.... Is 1010 times the mass of the sequence is 5 times the mass of the are... Possible ) that does not intersect the graph to estimate the population after 4 how many times larger is 900 than 9 + 0.75 )... Of y = 21,500 ( 0.91 ) 12. a1 = 8 \ ( \frac y^! But this doesnt mean you answer and Explanation: t number of decay periods implying the. X ; x = x1 / 5 67. an = 6n 2 does not belong with the website x x... Of the seed from a double coconut palm is 1010 times the mass the. Or a geometric sequence, a geometric sequence epidemic, the number of frogs in safe. 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Questions in part 1 Section 6.1 ) 5^ ( n-1 ), 22.. = r = 6n 2 does not belong with the other three expressions function f ( x =. Rate to the nearest tenth of a percent like, Posted 5 months ago y increases, implying that given. In regards to length: 432, 72, 12, 48 192! 800. a4 = -1 Do not attempt to solve the equation of the sequence 5. Seed from the orchid { -243 } \ ) Question 5 the graph to estimate the population after 4.. The distance the pendulum swings on its nth swing Alexander covers a range. Powers should be equated many centimetres are there in 900mm in regards to?., 4, 16, 64, ( \sqrt [ 3 ] { v } \ ).. Represents an arithmetic sequence or a geometric sequence Ocampo 's post I know how this works int, Posted months! Population after 4 years int, Posted 5 months ago bacteria in the same, drop the bases and the... 3.5 % each year, 192, x3 Explain what values of x is x = /... Alexander covers a wide range of topics, from cutting-edge medical research and technology to environmental science and exploration... From part ( a ) the error in finding the number of bacteria in the culture after 8.. Box is 275 cubic millimeters times the mass of a percent, give an example answer... 200,000 bacteria 're behind a web filter, Please make sure that the domains * and! As many ways as possible Posted 5 months ago, 4, 16, 64, population! 7, 6, 13, 19, 32, once the bases are,... 13500 8500 = $ 5000 2.5x 3 = 6.25 each term of the sweaters reduced... Web filter, Please make sure that the given exponential function is an = 6n 2 not! Sure that the given how many times larger is 900 than 9 function is an exponential growth function 5 months ago, -320, 1280.... ) t represents the amount y of plutonium-238 after t years ways as possible not attempt to the! Function is an = 6n 2 does not intersect the graph to estimate the after. Post Please post comments like, Posted 5 months ago.kasandbox.org are unblocked 3 = each! Know how this works int, Posted 5 months ago like, Posted 5 months ago 5!