1 6. Chapter 6 Algebra.pdf - Answer Key Chapter 6 College Algebra | OpenStax Try It 6.1 Exponential Functions 1 g(x = 0.875 \u2009andj(x = 1095.6 \u2009 represent. 13. This expression represents a variable cost because it changes according to the number of miles driven. Shifting the function right or left and reflecting the function about the y-axis will affect its domain. 7. Any root expression can be rewritten as an expression with a rational exponent so that the power rule can x 17. logc (k) = d The graph of G(x) APY = A(t)−a If sales continue at this rate, about 171,000 games will be sold in the year 2015. 6.3 Logarithmic Functions same base, then apply the logarithm to each side and use properties of logarithms to solve. −2.23266 29. Answer: 73 Section 2.3 1. (−∞, −2) = x+2 (x−3) x+2−6x+18 x 49. f (x) = 3log4 (x + 2) When f (x) = 8, x ≈ 15. While billion, or 1 million people. 708 What are the company’s monthly expenses? 6. f (x) = √2(√2) . 63. 13. p ≈ 2.67 7. not exponential; the charge decreases by a constant amount each visit, so the statement represents a 6 − ) 3 67. more than the width. Horizontal asymptote: h(x) = 3; Domain: all real numbers; Range: all real numbers strictly greater than 3. 17. 43. 17. k 17 = log ( C 6.8 Section Exercises = 25 log10 (1, 000, 000) = 6 B 31. b. A logarithm is an exponent. 11. x From the graph of the function f (x) Domain: (−∞, ) ; Range: (−∞, ∞) that might influence the long-term validity of the exponential growth model are drought, an epidemic that – Evaluate 53x when x 9. 19. f (x) = 2000(0.1) for 4. culls the population, and other environmental and biological factors. 31. below. 1+3.182e −0.545x 49. How many ft2 of new carpeting should be ordered? The screencast video solutions here are second to none. − (recalling that √121 1 = (121) 2 = 11 ) ) = −5 5. log(1, 000, 000) = 6 Domain: (1, ∞) ; Range: (−∞, ∞) ; Vertical asymptote: x → ∞ x-intercept: ( = 1; DNE 5. 47. f (x) = 0.82 25.081 C N (3) ≈ 71 The perimeter of a rectangular outdoor patio is [latex]54[/latex] ft. 3. a. The domain is (−∞, ∞) ; the range is (0, ∞) ; the horizontal asymptote is y = 0. 37. 4. log2 ( is equivalent to 106 n Terms. 41. about 88 minutes 3 8. 39. Find the area of the graph paper. 3 800.3333 45. h(−7) = −58 1.06 x A 6/38 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax 1. logb 2 + logb 2 + logb 2 + logb k = 3logb 2 + logb k 5 = log (11) Assign a variable to represent the unknown quantity. ln(7) (5) = log (5) 57. Note that we could have cleared the fractions in the equation by multiplying both sides of the equation by the LCD to solve for [latex]r[/latex]. −1 1. exponential decay; The growth factor, 0.825, is between 0 and 1. We can use these quantities to model an equation that can be used to find the daily car rental cost [latex]C[/latex]. An asymptote is a line that the graph of a function approaches, as x either increases or decreases without If the average number of minutes used each month is 420, then Company A offers a lower monthly cost of $55 compared to Company B’s monthly cost of $56.80. Next graph the scatter plot using the STAT PLOT feature. 14. ln 8 If spending continues at this rate, the graduate’s credit card debt will be $4,499.38 after one year. The domain is (2, ∞) ,the range is (−∞, ∞) , and the vertical asymptote is x C Domain: (− 17 E 51. final answer to quickly see if you got it right. The difference in magnitudes was about 3.929. b − 1 (x + 2) − log6 (x − 3) = log6 ( x+2 = e 10. x D 4 x ) ; y-intercept: (0, 2) ; Domain: all real numbers; Range: all real numbers greater than 0. y-intercept: (0, −2) 13. logb (7) 61. 2. log3 (x + 3) − log3 (x − 1) − log3 (x − 2) His drive home takes 40 min, or [latex]\frac{2}{3}[/latex] h, and his speed averages 10 mi/h less than the morning drive. The answer should be very close to larger than forest A and will remain that way as long as the population growth models hold. 36 10. x = 1 1 12. n > 0,f (x) = a ⋅ ( 365 r The volume is [latex]1,600[/latex] cubic inches. 43. g(6) = 800 + x 1.4142(1.4142) . −k ln(4) To verify, suppose x = 0 is in the domain of the The shape of the data points on the scatter graph y = 2e0.5x . Let Shaun −3 43. x = ± 45. x = 10 10 Thus, the annual percentage rate does not or 2 orders of magnitude greater, than the mass of Earth. The problem is stated, a formula is identified, the known quantities are substituted into the formula, the equation is solved for the unknown, and the problem’s question is answered. The exponential regression model that fits these data is y = 522.88585984(1.19645256) . 11 5 ) = 31. 7. y ≈ 12 ⋅ 1.85x B 37. f (t) = 1350e(0.03466t) ; after 3 hours: P (180) ≈ 691, 200 2 − −12 x−4 > 0 . 55. a a(1+ 365(1) r ) 365 = a[(1+ −a = a 1 65. = −1 3. x = 1 x Answers will vary. value. 3 log ( 3 1 6 = 0 = 0 = 0 = : x+2 Neither The graphs of f (x) = log x−3 2 S 2. n b x )b is the horizontal shift f (x − n). since you will see how Shaun Dychko made the calculation. −x 5. x = − 7. n = 11 b ) log (11) The length is [latex]3[/latex] ft. greater than the width. 5 29. log11 log ( ( 6 log (b) = 4. . 47. = 125 is equivalent to log5 (125) = 3 25/38 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax 49. and [latex]W=9[/latex] in. If the sum of the two numbers is [latex]36[/latex], find the numbers. Doubling time is a measure of growth and is thus associated with exponential growth models. plug it into your calculator. inverse exponential function. A horizontal asymptote would suggest a limit on the range, and the range of any logarithmic function −2 ln(x) 11. exponential; f (x) = 1.2 The two numbers are [latex]7[/latex] and [latex]24[/latex]. As x → −∞ , f (x) → ∞ 31. 41. = − 8 3 ln( 38 )−8 19. x = 21. x = ln 12 23. x ) − 7 ln(38) 3 9 ln( = 3 1. b. The sum of the two numbers is 31. log(x) + 21. ln(2x 7 14 Rewriting as an exponential x−3 x−3 37. 21. logn (103) = ln 0.5 29. exceed forest B, but because forest B actually grows at a faster rate, the population will eventually become So, Company B offers the lower monthly cost of $86.40 as compared with the $92 monthly cost offered by Company A when the average number of minutes used each month is 1,160. 2. less than 230 years, 229.3157 to be exact Specifically, it is the exponent to which a base b is raised to produce a given Logistic models are best used for situations that have limited values. 2 4. If the population continues to grow at this rate, there will be about 25,634 seals in 2020. 47. f (−1) ≈ −0.2707 33. f (x) = 4 − 3 About 38 wolves x 8. 21. Then, x ln(y) = ln(b ) 12. x Therefore, x = 0 is not = − 1 Write an equation interpreting the words as mathematical operations. The company has monthly operating expenses of $350 for utilities and $3,300 for salaries. rewritten as a single logarithm with the same base. Simplify: 1 8 9 . more than twice the width. 15. en = w Be sure the solution can be explained in words including the units of measure. Domain: (−∞, 0) ; Range: (−∞, ∞) ; Vertical asymptote: x 7. ln x 9. x 11 Domain: (5, ∞) ; Vertical asymptote: x = C 9/38 9/27/2020 Answer Key Chapter 6 - College Algebra | OpenStax 13. = 1 15 log(x) + 13 log(y) − 19 log(z) Then there is some number n such that n = log(0).
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