Please do problems #24, 25, 26, 29, 32, 34, 37, 40, 42, 50, 51, 54, 55, 59

Math 155 Lab (4.4-4.7).pdf Q CHAPTER 4 REVIEW 435 21. Evaluate In(e-0.8648) without using a calculator. 22. Evaluate In(V18 ) using a calculator. Round to the nearest thousandth. GRAPHS OF LOGARITHMIC FUNCTIONS 23. Graph the function g(x) = log(7x + 21) - 4. 24. Graph the function h(x) = 21n(9 - 3x) + 1. 25. State the domain, vertical asymptote, and end behavior of the function g (x) = In(4x + 20) - 17. LOGARITHMIC PROPERTIES 26. Rewrite In(7r . 1 1st) in expanded form. 27. Rewrite log,(x) + log, (5) + log; (y) + log, (13) in compact form. 28. Rewrite log.( 83 ) in expanded form. 29. Rewrite In(z) - In(x) - In(y) in compact form. 30. Rewrite In ( 5 ) as a product. 31. Rewrite -log,( 17 ) as a single logarithm. 32. Use properties of logarithms to expand log S" 33. Use properties of logarithms to expand In( 26 \\/ B+ !). 34. Condense the expression 5In(b) + In(c) + In(4 - a) log u to a single logarithm. 2 35. Condense the expression 3log,v + 6log w to a single logarithm 36. Rewrite log, (12.75) to base e. 37. Rewrite 512x - 17 = 125 as a logarithm. Then apply the change of base formula to solve for x using the common log. Round to the nearest thousandth. EXPONENTIAL AND LOGARITHMIC EQUATIONS 38. Solve 2163x . 216* = 363x +2 by rewriting each side 39. Solve 125 = 53 by rewriting each side with a with a common base. 625 common base. 40. Use logarithms to find the exact solution for 41. Use logarithms to find the exact solution for 7 . 17-9x - 7 = 49. If there is no solution, write no 3ebn -2 + 1 = -60. If there is no solution, write no solution. solution. 42. Find the exact solution for 5ex - 4 = 6 . If there is 43. Find the exact solution for 2e5x -2 - 9 = -56. no solution, write no solution. If there is no solution, write no solution. 44. Find the exact solution for 52x - 3 = 7*+1. If there is 45. Find the exact solution for ex - ex - 110 = 0. If no solution, write no solution. there is no solution, write no solution. 46. Use the definition of a logarithm to solve. 47. Use the definition of a logarithm to find the exact -5log (10n) = 5. solution for 9 + 6In(a + 3) = 33. 48. Use the one-to-one property of logarithms to find 49. Use the one-to-one property of logarithms to find an exact solution for log, (7) + logs (-4x) = log, (5). an exact solution for In(5) + In(5x2 - 5) = In(56). If If there is no solution, write no solution. there is no solution, write no solution. 50. The formula for measuring sound intensity in 51. The population of a city is modeled by the equation decibels D is defined by the equation D = 10log P(t) = 256, 1140.25 where t is measured in years. If 7 . where I is the intensity of the sound in watts the city continues to grow at this rate, how many years will it take for the population to reach one per square meter and I, = 10-12 is the lowest level of million? sound that the average person can hear. How many decibels are emitted from a large orchestra with a sound intensity of 6.3 . 10- watts per square meter? 52. Find the inverse function f- for the exponential 53. Find the inverse function f for the logarithmic function f(x) = 2 . ex +1 - 5. function f(x) = 0.25 . log,(x3 + 1).436 CHAPTER 4 EXPONENTIAL AND LOGARITHMIC FUNCTIONS EXPONENTIAL AND LOGARITHMIC MODELS For the following exercises, use this scenario: A doctor prescribes 300 milligrams of a therapeutic drug that decays by about 17% each hour. 54. To the nearest minute, what is the half-life of the drug? 55. Write an exponential model representing the amount of the drug remaining in the patient's system after 1 hours. Then use the formula to nd the amount of the drug that would remain in the patient's system after 24 hours. Round to the nearest hundredth ofa gram. For the following exercises, use this scenario: A soup with an internal temperature of 350 Fahrenheit was taken off the stove to cool in a 71F room. After fteen minutes. the internal temperature ofthe soup was 175F. 55. Use Newton's Law of Cooling to write a formula that 57. How many minutes will it take the soup to cool models this situation. to 85F? 1200 W\" models the number of people in a e For the following exercises, use this scenario: The equation N0) = school who have heard a rumor after tdays. 53. How many people started the rumor? 59. To the nearest tenth, how many days will it be before the rumor spreads to half the carrying capacity? 50. What is the carrying capacity? For the following exercises, enter the data from each table into a graphing calculator and graph the resulting scatter plots. Determine whether the data from the table would likely represent a function that is linear, exponential, or logarithmic. 51, x l 2 3 4 5 6 7 8 9 10 f[x) 3.05 4.42 6.4 9.28 13.46 19.52 28.3 41.04 59.5 86.28 62. x 0.5 1 3 5 7 10 12 13 15 17 20 f(x) 18.05 17 15.33 14.55 14.04 13.5 13.22 13.1 12.88 12.69 12.45 63. Find a formula for an exponential equation that goes through the points (2. 100) and (0,4). Then express the formula as an equivalent equation with base c. FITTING EXPONENTIAL MODELS T0 DATA 64. What is the carrying capacity for a population modeled by the logistic equation PU) : f$9903i31 ? What is the initial population for the model? 65. The population ofa culture of bacteria is modeled by the logistic equation PU) : \"12%. where t is in e f days. To the nearest tenth, how many days will it take the culture to reach 75% of its carrying capacity? For the following exercises, use a graphing utility to create a scatter diagram of the data given in the table. Observe the shape of the scatter diagram to determine whether the data is best described by an exponential, logarithmic, or logistic model. Then use the appropriate regression feature to nd an equation that models the data. When necessary, round values to ve decimal places. 66. x 1 2 3 4 5 6 7 8 9 10 x} 409.4 260.7 170.4 110.6 74 44.7 32.4 19.5 12.7 8.1 67- x 0.15 0.25 0.5 0.75 1 1.5 2 2.25 2.75 3 3.5 x) 36.21 28.88 24.39 18.28 16.5 12.99 9.91 8.57 7.23 5.99 4.81 68. x 0 2 4 5 7 8 10 ll 15 17 at) 9 22.6 44.2 62.1 96.9 113.4 133.4 137.6 148.4 149.3