Test Bank For College Mathematics for Business, Economics, Life Sciences, and Social Sciences, 14th Edition

Exam Name___________________________________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Use point-by-point plotting to sketch the graph of the equation. 1) y = x – 5 1) _______ A) B) C) D) 2) y = -3 2) _______ A) B) C) D) Determine whether the graph is the graph of a function. 3) 3) _______ A) function B) not a function 4) 4) _______ A) function B) not a function 5) 5) _______ A) function B) not a function Determine whether the relation represents a function. If it is a function, state the domain and range. 6) 6) _______ A) function domain:{20, 45, 70, 95} range: {4, 9, 14, 19} B) function domain: {4, 9, 14, 19} range: {20, 45, 70, 95} C) not a function 7) 7) _______ A) function domain: {carrots, peas, squash} range: {Bob, Ann, Dave} B) function domain: {Bob, Ann, Dave} range: {carrots, peas, squash} C) not a function 8) {(41, -3), (5, -2), (5, 0), (9, 2), (21, 4)} 8) _______ A) function domain: {41, 9, 5, 21} range: {-3, -2, 0, 2, 4} B) function domain: {-3, -2, 0, 2, 4} range: {41, 9, 5, 21} C) not a function 9) {(-3, 10), (-2, 5), (0, 1), (2, 5), (4, 17)} 9) _______ A) function domain: {-3, -2, 0, 2, 4} range: {10, 5, 1, 17} B) function domain: {10, 5, 1, 17} range: {-3, -2, 0, 2, 4} C) not a function Determine whether the function is linear, constant, or neither 10) y = 10) ______ A) Linear B) Constant 11) y = A) Linear +8 11) ______ B) Constant C) Neither 12) y = 12) ______ A) Linear B) Constant 13) y – 12 = 0 13) ______ C) Neither C) Neither A) Linear B) Constant C) Neither Use point-by-point plotting to sketch the graph of the equation. 14) f(x) = 14) ______ A) B) C) D) The graph of a function f is given. Use the graph to answer the question. 15) Use the graph of f given below to find f(-5). 15) ______ A) -5 B) 3 C) 8 D) 0 Find the function value. 16) Find f(-9) when f(x) = 5 – 7 . 16) ______ A) 572 B) -562 C) 68 D) 131 17) f(x) = ; f(-2) 17) ______ A) – B) C) D) 4 18) Given that f(x) = 5 A) 5 – 18t + 16 B) – 2x, find f(t + 2). + 2t – 6 C) 3t + 6 18) ______ D) 5 + 18t + 16 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Provide an appropriate response. 19) If g(x) = + x – 9, find g(-2), g(1), and g 20) For f(t) = 3t + 2 and g(t) = 2 – . 19) _____________ , find 4f(3) – g(-3) + g(0). 21) For f(t) = 3 – 5t, find . 20) _____________ 21) _____________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Compute and simplify the difference quotient 22) f(x) = 5 A) 10x + 7 + 7x , h ≠ 0. 22) ______ B) 10x + 5h + 7 C) 10 + 5h+ 7x D) 15x – 7h + 14 Determine the domain of the function. 23) f(x) = – 7x + 923) ______ A) No solution B) All real numbers except C) All real numbers 24) f(x) = D) x ≤ 24) ______ A) No solution B) All real numbers except 2 C) All real numbers D) x < 2 25) f(x) = 25) ______ A) x ≤ 3 B) All real numbers except 3 C) x < 3 D) No solution 26) f(x) = 26) ______ A) All real numbers B) x 0 78) ______ A) -0.93 < x < 2.46 B) x 0.93 C) x 2.46 D) -2.46 < x < 0.93 79) 1.5 – 4.7x – 2.9 ≤ 0 79) ______ A) x 0.53 B) x 3.66 C) -3.66 < x < 0.53 D) -0.53 < x g(x) using parts i and ii; (iv) solve f(x) < g(x) using parts i and ii. 83) f(x) = -0.8x(x – 8), g(x) = 0.4x + 3.2; 0 ≤ x ≤ 10 83) ______ A) (i) f is the curve, g is the line (ii) 0.61, 7.02 (iii) 0.61 < x < 7.02 (iv) 0 ≤ x < 0.61 or 7.02 < x ≤ 8 B) (i) f is the curve, g is the line (ii) 0.58, 6.92 (iii) 0.58 < x < 6.92 (iv) 0 ≤ x < 0.58 or 6.92 < x ≤ 8 C) (i) f is the curve, g is the line (ii) 0.58, 7.98 (iii) 0.58 < x < 7.98 (iv) 0 ≤ x < 0.58 or 7.98 < x ≤ 8 D) (i) f is the curve, g is the line (ii) 0.61, 7.98 (iii) 0.61 < x < 7.98 (iv) 0 ≤ x < 0.61 or 7.98 < x ≤ 8 Solve the problem. 84) In economics, functions that involve revenue, cost and profit are used. Suppose R(x) and C(x) denote the total revenue and the total cost, respectively, of producing a new high-tech widget. The difference total profit for producing x widgets. Given R(x) = 60x – 0.4 ______ A) P(x) = 60x – 0.4 C) P(x) = -0.4 B) P(x) = -0.4 + 57x – 13 and represents the find the equation for P(x). 84) + 63x + 13 D) P(x) = 3x + 13 85) In economics, functions that involve revenue, cost and profit are used. Suppose R(x) and C(x) denote the total revenue and the total cost, respectively, of producing a new high-tech widget. The difference total profit for producing x widgets. Given R(x) = 60x – 0.4 A) 55687 and find P(100). represents the 85) ______ B) 313 C) 2000 D) 1687 86) A professional basketball player has a vertical leap of 37 inches. A formula relating an athlete's vertical leap V, in inches, to hang time T, in seconds, is V= A) 1 sec B) 0.6 sec C) 0.9 sec . What is his hang time? Round to the nearest tenth. 86) ______ D) 0.8 sec 87) Under certain conditions, the power P, in watts per hour, generated by a windmill with winds blowing v miles per hour is given by P(v) = 0.015 . Find the power generated by 18-mph winds. 87) ______ A) 4.86 watts per hour B) 0.00006075 watts per hour C) 58.32 watts per hour D) 87.48 watts per hour 88) The U. S. Census Bureau compiles data on population. The population (in thousands) of a southern city can be approximated by P(x) = 0.08 population about 804,200? – 13.08x + 927, where x corresponds to the years after 1950. In what calendar year was the 88) ______ A) 1965 B) 2000 C) 1955 D) 1960 89) Assume that a person's critical weight W, defined as the weight above which the risk of death rises dramatically, is given by W(h) = , where W is in pounds and h is the person's height in inches. Find the tcritical weight for a person who is 6 ft 11 in. tall. Round to the nearest tenth. A) 212.4 lb B) 221.5 lb C) 377.4 lb 89) ______ D) 339.3 lb 90) The polynomial gives the approximate total earnings of a company, in millions of dollars, where x represents the number of years since 1996. This model is valid for the years from 1996 to 2000. Determine the earnings for 2000. Round to 2 decimal places. 90) ______ A) $2.26 million B) $2.82 million C) $2.03 million D) $2.36 million Use the REGRESSION feature on a graphing calculator. 91) The average retail price in the Spring of 2000 for a used Camaro Z28 coupe depends on the age of the car as shown in the following table. Find the quadratic model that best estimates this data. Round your answer to whole numbers. A) y = 102 – 2576x + 20,669 C) y = 102 – 2576x 91) ______ B) y = -1551x + 18,790x D) y = -9 + 235 – 3134x + 21,252 92) As the number of farms has decreased in South Carolina, the average size of the remaining farms has grown larger, as shown below. Let x represent the number of years since 1900. Use a graphing calculator to fit a quadratic function to the data. Round your answer to five decimal places. 92) ______ A) y = 0.02536 + 1.21114 x + 102.58741 B) y = -.00114 + 0.19605 C) y = 0.02536 + 1.21114 + 102.58741 D) y = 0.02536 + 1.21114 x + 102.58741 – 5.29775 + 143.55245 93) Since 1984 funeral directors have been regulated by the Federal Trade Commission. The average cost of a funeral for an adult in a Midwest city has increased, as shown in the following table. Let x represent the number of years since 1980. Use a graphing calculator to fit a quartic function to the data. Round your answer to five decimal places. 93) ______ A) y = 170.5971x + 1991.5213 B) y = -2.047489 + 212.82699x + 1879.85469 C) y = -0.04268 + 1.53645 – 16.76289 + 231.82723x + 1927.58518 D) y = -0.04268 Solve the problem. 94) The population P, in thousands, of Fayetteville is given by population at 9 months. 94) ______ A) 7988 B) 15, 976 C) 40,000 D) 30, 769 P(t) = , where t is the time, in months. Find the 95) If the average cost per unit C(x) to produce x units of plywood is given by units? 95) ______ A) $24.00 B) $120.00 C) $80.00 what is the unit cost for 10 D) $3.00 96) Suppose the cost per ton, y, to build an oil platform of x thousand tons is approximated by the cost per ton for 96) ______ A) $16.67 C) $7083.33 B) $425.00 What is D) $467.03 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 97) The financial department of a company that produces digital cameras arrived at the following price-demand function and the corresponding revenue function: p(x) = 95.4 – 6x price-demand R(x) = x ∙ p(x) = x(95.4 – 6x) revenue function The function p(x) is the wholesale price per camera at which x million cameras can be sold and R(x) is the corresponding revenue (in million dollars). Both functions have domain 1 ≤ x ≤ 15. They also found the cost function to be C(x) = 150 + 15.1x (in million dollars) for manufacturing and selling x cameras. Find the profit function and determine the approximate number of cameras, rounded to the nearest hundredths, that should be sold for maximum profit. 97) _____________ 98) The financial department of a company that manufactures portable MP3 players arrived at the following daily cost equation for manufacturing x MP3 players per day: The average cost per unit at a production level of players per day is (A) Find the rational function . (B) Graph the average cost function on a graphing utility for 10 ≤ x ≤ 200. (C) Use the appropriate command on a graphing utility to find the daily production level (to the nearest integer) at which the average cost per player is a minimum. What is the minimum average cost (to the nearest cent)? 98) _____________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. For the polynomial function find the following: (i) Degree of the polynomial; (ii) All x intercepts; (iii) The y intercept. 99) y = 8x + 5 99) ______ A) (i) 1 (ii) (iii) 8 B) (i) 1 (ii) (iii) 5 (ii) C) (i) 1 (iii) 5 (ii) 5 D) (i) 1 (iii) 100) y = – 49 100) _____ A) (i) 2 (ii) -7, 7 (iii) -49 B) (i) 1 (ii) 7 (iii) -49 C) (i) 1 (ii) 24.5 (iii) -49 D) (i) 2 (ii) -8, 8 (iii) -49 101) y = + 5x – 50 A) (i) 2 (ii) -10, 1 (iii) -50 B) (i) 2 (ii) -10, 5 (iii) -50 C) (i) 2 (ii) 10, 5 (iii) -50 D) (i) 2 (ii) 10, -5 (iii) -50 101) _____ 102) y = 18 + 3x A) (i) 2 (ii) 6, 3 (iii) 18 B) (i) 2 (ii) 6, -3 (iii) 18 C) (i) 2 (ii) -3, -6 (iii) -18 D) (i) 2 (ii) 3, -6 (iii) -18 102) _____ 103) y = (x + 10)(x + 6)(x + 6) A) (i) 3 (ii) -10, -6, -6 (iii) 360 B) (i) 3 (ii) -10, -6, -6 (iii) -36 C) (i) 3 (ii) 10, 6, 6 (iii) 36 D) (i) 3 (ii) 10, 6, 6 (iii) 360 103) _____ 104) f(x) = ( 104) _____ + 7)( + 9) A) (i) 60 (ii) 7, 9 (iii) -63 B) (i) 16 (ii) none (iii) 63 C) (i) 16 (ii) 7, 9 (iii) 63 D) (i) 60 (ii) none (iii) -63 The graph that follows is the graph of a polynomial function. (i) What is the minimum degree of a polynomial function that could have the graph? (ii) Is the leading coefficient of the polynomial negative or positive? 105) 105) _____ A) (i) 3 (ii) Positive (ii) Positive (ii) Negative (ii) Negative B) (i) 2 C) (i) 3 D) (i) 2 106) 106) _____ A) (i) 2 (ii) Negative (ii) Positive (ii) Positive (ii) Negative 107) B) (i) 3 C) (i) 2 D) (i) 3 107) _____ A) (i) 3 (ii) Positive (ii) Negative (ii) Negative (ii) Positive B) (i) 3 C) (i) 4 D) (i) 4 108) 108) _____ A) (i) 2 (ii) Negative (ii) Positive (ii) Negative (ii) Positive B) (i) 1 C) (i) 1 D) (i) 2 109) 109) _____ A) (i) 4 (ii) Positive B) (i) 4 (ii) Negative (ii) Negative (ii) Positive C) (i) 3 D) (i) 3 Provide an appropriate response. 110) What is the maximum number of x intercepts that a polynomial of degree 10 can have? A) 10 B) 11 C) 9 D) Not enough information is given. 110) _____ 111) What is the minimum number of x intercepts that a polynomial of degree 11 can have? Explain. A) 0 because a polynomial of odd degree may not cross the x axis at all. B) 1 because a polynomial of odd degree crosses the x axis at least once. C) 11 because this is the degree of the polynomial. D) Not enough information is given. 111) _____ 112) What is the minimum number of x intercepts that a polynomial of degree 8 can have? Explain. A) 1 because a polynomial of even degree crosses the x axis at least once. B) 0 because a polynomial of even degree may not cross the x axis at all. C) 8 because this is the degree of the polynomial. D) Not enough information is given. 112) _____ For the rational function below (i) Find the intercepts for the graph; (ii) Determine the domain; (iii) Find any vertical or horizontal asymptotes for the graph; (iv) Sketch any asymptotes as dashed lines. Then sketch the graph of y = f(x). 113) f(x) = 113) _____ A) (i) x intercept: -2; y intercept: 2 (ii) Domain: all real numbers except -1 (iii) Vertical asymptote: x = -1; horizontal asymptote: y = 1 (iv) B) (i) x intercept: 0; y intercept: 0 (ii) Domain: all real numbers except 1 (iii) Vertical asymptote: x = 1; horizontal asymptote: y = 1 (iv) C) (i) x intercept: 2; y intercept: 2 (ii) Domain: all real numbers except 1 (iii) Vertical asymptote: x = 1; horizontal asymptote: y = 1 (iv) D) (i) x intercept: 0; y intercept: 0 (ii) Domain: all real numbers except -1 (iii) Vertical asymptote: x = -1; horizontal asymptote: y = 1 (iv) 114) f(x) = 114) _____ A) (i) x intercept: 5; y intercept: (ii) Domain: all real numbers except 4 (iii) Vertical asymptote: x = 4; horizontal asymptote: y = 1 (iv) B) (i) x intercept: -3; y intercept: (ii) Domain: all real numbers except -4 (iii) Vertical asymptote: x = -4; horizontal asymptote: y = 1 (iv) C) (i) x intercept: -5; y intercept: (ii) Domain: all real numbers except -4 (iii) Vertical asymptote: x = -4; horizontal asymptote: y = 1 (iv) D) (i) x intercept: 3; y intercept: (ii) Domain: all real numbers except 4 (iii) Vertical asymptote: x = 4; horizontal asymptote: y = 1 (iv) 115) f(x) = 115) _____ A) (i) x intercept: 0; y intercept: 0 (ii) Domain: all real numbers except 2 (iii) Vertical asymptote: x = 2; horizontal asymptote: y = -3 (iv) B) (i) x intercept: 0; y intercept: 0 (ii) Domain: all real numbers except 2 (iii) Vertical asymptote: x = 2; horizontal asymptote: y = 3 (iv) C) (i) x intercept: 0; y intercept: 0 (ii) Domain: all real numbers except -2 (iii) Vertical asymptote: x = -2; horizontal asymptote: y = 3 (iv) D) (i) x intercept: 0; y intercept: 0 (ii) Domain: all real numbers except -2 (iii) Vertical asymptote: x = -2; horizontal asymptote: y = -3 (iv) 116) f(x) = 116) _____ A) (i) x intercept: ; y intercept: (ii) Domain: all real numbers except 2 (iii) Vertical asymptote: x = 2; horizontal asymptote: y = -2 (iv) B) (i) x intercept: ; y intercept: (ii) Domain: all real numbers except 2 (iii) Vertical asymptote: x = 2; horizontal asymptote: y = -2 (iv) C) (i) x intercept: – ; y intercept: (ii) Domain: all real numbers except -2 (iii) Vertical asymptote: x = -2; horizontal asymptote: y = -2 (iv) D) (i) x intercept: – ; y intercept: (ii) Domain: all real numbers except -2 (iii) Vertical asymptote: x = -2; horizontal asymptote: y = -2 (iv) For the rational function below (i) Find any intercepts for the graph; (ii) Find any vertical and horizontal asymptotes for the graph; (iii) Sketch any asymptotes as dashed lines. Then sketch a graph of f. 117) y = 117) _____ A) (i) y intercept: – 2 (ii) horizontal asymptote: y = 0 (iii) B) (i) y intercept: -6 (ii) horizontal asymptote: y = 0; vertical asymptotes: x = 6 and x = -6 (iii) C) (i) y intercept: 6 (ii) horizontal asymptote: y = 0; vertical asymptotes: x = 6 and x = -6 (iii) D) (i) y intercept: – 2 (ii) horizontal asymptote: y = 0; vertical asymptotes: x = 3 and x = -3 (iii) Sketch the graph of the function. 118) f(x) = 118) _____ A) B) C) D) 119) f(x) = 119) _____ A) B) C) D) Find the equation of any horizontal asymptote. 120) f(x) = 120) _____ A) y = 0 B) y = C) y = 121) f(x) = 121) _____ A) y = -6 B) y = 6 C) y = 1 D) None 122) f(x) = 122) _____ A) y = 8 B) y = 3 C) None D) None D) y = -4 Find the equations of any vertical asymptotes. 123) f(x) = 123) _____ A) y = 1, y = -4 B) y = 3 C) x = -1, x = 4 D) x = 1, x = -4 124) f(x) = 124) _____ A) x = 10, x = -10 B) x = -5C) y = 5, y = -8 D) x = 5, x = -8 125) f(x) = 125) _____ A) x = 6, x = -4 B) x = 6 C) x = -6, x = 4 126) f(x) = D) None 126) _____ A) x = 2, x = -2 B) x = -8C) x = 8 D) None Write an equation for the lowest-degree polynomial function with the graph and intercepts shown in the figure. 127) 127) _____ A) f(x) = + 5x + 6 B) f(x) = – 6x + 5 C) f(x) = + 6x + 5 D) f(x) = + 5x – 6 128) 128) _____ A) f(x) = + 9x – 10 B) f(x) = + 9x + 10 C) f(x) = + 10x + 9 D) f(x) = – – 10x – 9 129) 129) _____ A) f(x) = – – 16x B) f(x) = – + 16x C) f(x) = – – 16x D) f(x) = + 16x Solve the problem. 130) Financial analysts in a company that manufactures ovens arrived at the following daily cost equation for manufacturing x ovens per day: C(x) = + 4x + 1800. The average cost per unit at a production level of x ovens per day is (x) = C(x)/x. (i) Find the rational function . (ii) Sketch a graph of (x) for 10 ≤ x ≤ 125. (iii) For what daily production level (to the nearest integer) is the average cost per unit at a minimum, and what is the minimum average cost per oven (to the nearest cent)? HINT: Refer to the sketch in part (ii) and evaluate minimum value is found. 130) _____ (x) at appropriate integer values until a A) (i) (ii) (x) = (iii) 61 units; $133.29 per oven (ii) B) (i) (x) = D) (i) (x) = (iii) 42 units; $88.86 per oven C) (i) (ii) (x) = (iii) 44 units; $185.61 per oven (ii) (iii) 22 units; $48.93 per oven Graph the function. 131) f(x) = 131) _____ A) B) C) D) 132) f(x) = +2 132) _____ A) B) C) D) 133) f(x) = -3 133) _____ A) B) C) D) 134) f(x) = 134) _____ A) B) C) D) 135) f(x) = 135) _____ A) B) C) D) Solve the equation. 136) Solve for x: A) -1 B) 1 C) 9 136) _____ D) 3 137) Solve for x: = 137) _____ A) 5 B) 15 C) -5 D) -15 138) Solve for x: ∙ A) {4} B) {5, 4} C) {-5, -4} = 138) _____ D) {5} 139) Solve for t: = 0.05 Round your answer to four decimal places. A) -66.4815 B) -70.1312 C) 44.321 D) 42.7962 139) _____ SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the problem. 140) In the table below, the amount of the U.S. minimum wage is listed for selected years. Find an exponential regression model of the form y = a ∙ , where y represents the U.S. minimum wage x years after 1960. Round a and b to four decimal places. According to this model, what will the minimum wage be in 2005? In 2010? 140) ____________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. 141) Hi-Tech UnWater begins a cable TV advertising campaign in Miami to market a new water. The percentage of the target market that buys water is estimated by the function t represents the number of days of the campaign. After how long will 90% of the target market have bought the water? 141) _____ A) 90 days B) 120 days C) 115 days D) 3 days 142) The number of books in a community college library increases according to the function measured in years. How many books will the library have after 8 year(s)? 142) _____ where t is A) 4462 B) 7200 C) 9153 D) 10,275 143) Since life expectancy has increased in the last century, the number of Alzheimer's patients has increased dramatically. The number of patients in the United States reached 4 million in 2000. Using data collected since 2000, it has been found that the data can be modeled by the exponential function 2000. Estimate the Alzheimer's patients in 2025. Round to the nearest tenth. A) 8.0 million B) 3.9 million C) 4.8 million where x is the years since 143) _____ D) 7.8 million 144) A sample of 800 grams of radioactive substance decays according to the function where t is the time in years. How much of the substance will be left in the sample after 10 years? Round to the nearest whole gram. 144) _____ A) 9 grams B) 605 grams C) 800 grams D) 1 gram 145) The number of reports of a certain virus has increased exponentially since 1960. The current number of cases can be approximated using the function the year 2010. 145) _____ where t is the number of years since 1960. Estimate the of cases in A) 266 B) 207 C) 190 D) 240 146) An initial investment of $12,000 is invested for 2 years in an account that earns 4% interest, compounded quarterly. Find the amount of money in the account at the end of the period. 146) _____ A) $994.28 B) $12,865.62 C) $12,994.28 D) $12,979.20 147) Suppose that $2200 is invested at 3% interest, compounded semiannually. Find the function for the amount of money after t years. 147) _____ A) A = 2200 B) A = 2200 C) A = 2200 D) A = 2200 Use the REGRESSION feature on a graphing calculator. 148) A strain of E-coli Beu-recA441 is placed into a petri dish at Celsius and allowed to grow. The following data are collected. Theory states that the number of bacteria in the petri dish will initially grow according to the law of uninhibited growth. The population is measured using an optical device in which the amount of light that passes through the petri dish is measured. Find the exponential equation in the form y = a ∙ 148) _____ A) y = C) y = 0.0903 ∙ , where x is the hours of growth. Round to four decimal places. B) y = 1.3384 ∙ D) y = 149) The total cost of the Democratic and the Republican national conventions has increased 596% over the 20-year period between 1980 and 2004. The following table lists the total cost, in millions of dollars, for selected years. Find the exponential functions that best estimates this data. Round your answer to four decimal places 149) _____ A) y = 6.6643x + 2.8857 B) y = 22.2887x∙ ( C) y = 1.0929 ∙ ( D) y = 22.2887 ∙ ( SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. 150) A particular bacterium is found to have a doubling time of 20 minutes. If a laboratory culture begins with a population of 300 of this bacteria and there is no change in the growth rate, how many bacteria will be present in 55 minutes? Use six decimal places in the interim calculation for the growth rate. 150) ____________ MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Convert to a logarithmic equation. 151) =8 151) _____ A) 3=8 B) 152) = 25 152) _____ A) 2 = 8=2 25 B) 2 = 153) =3 A) 0.4771 = log 10 5 =7 2=3 C) 25 = D) 8=3 2 D) 5 = 25 153) _____ B) 0.4771 = log 3 C) 3 = log 0.4771D) 0.4771 = 154) C) 10 154) _____ A) ln t = 7 B) t=e C) ln 7 = t D) e=t Convert to an exponential equation. 155) A) 27 = = B) 9 = 156) A) 155) _____ 512 = t = 512 B) C) 27 = 156) _____ =t C) 157) ln 44 = 3.7842 157) _____ A) B) = ln 44 D) 27 = = 512 = 44 C) D) =t = 3.7842 D) =1 Evaluate. 158) A) 4 158) _____ B) C) 32 D) 8 Use a calculator to evaluate the expression. Round the result to five decimal places. 159) log 0.17 159) _____ A) -1.76955 B) -1.77196 C) -0.76955 D) -4.07454 160) log 0.234 A) 1.26364 160) _____ B) -0.63074 C) 0.234D) -1.45243 161) log 51.237 161) _____ A) 51.237 B) 3.93646 C) 1.70958 D) Undefined 162) log (-10.25) 162) _____ A) -1.01072 B) 1.01072 C) 2.32728 D) Undefined 163) 36.8 163) _____ A) 3.60550 B) 1.56585 C) 1.73388 D) 0.57674 164) ln 0.027 A) 0.56864 164) _____ B) -3.61192 C) -1.56864 D) Undefined 165) ln 1097 A) 4.69775 165) _____ B) 3.04021 C) 9.30292 D) 7.00033 Write in terms of simpler forms. 166) XY A) X+ 166) _____ Y B) 167) 167) _____ A) B) 168) 168) _____ A) M 9 169) A) b+ B) M + 9 X- Y C) X- Y D) y C) b-y D) b- y C) 9 M D) 9 + 169) _____ B) C) D) Solve for x to two decimal places (using a calculator). 170) 700 = 500 170) _____ A) 1.35 B) 1.40 C) 520 D) 8.58 171) 5.2 = 171) _____ A) 1.07 B) 5.17 C) 2.32 D) 22.97 Use the properties of logarithms to solve. 172) A) 2 x+ B) 24 (x – 2) = C) 7 D) 6 173) x- 5= 24 2- 172) _____ (x – 3) 173) _____ M X+ Y A) 3 B) 2 174) A) 6 (x + 3) + x= B) -6 C) -6, -3 D) 3 175) A) 7 C) 2, 5 D) 5 (4x – 5) = 1 B) C) 54 174) _____ 175) _____ D) 176) ln (3x – 4) = ln 20 – ln (x – 5) 176) _____ A) -5, – B) 0, C) 177) log (x + 10) – log (x + 4) = log x A) 2 B) -5 C) 2, – 5 D) 6 178) log (x – 9) = 1 – log x 178) _____ A) -10, 1 B) 10 C) -1, 10 D) 5, 177) _____ D) -10 Graph by converting to exponential form first. 179) y = (x – 2) 179) _____ A) B) C) D) 180) y = (x + 1) 180) _____ A) B) C) D) Graph the function using a calculator and point-by-point plotting. Indicate increasing and decreasing intervals. 181) f(x) = 3 ln x 181) _____ A) Increasing: (0, ∞) B) Decreasing: (0, ∞) C) Decreasing: (0, ∞) D) Increasing: (-3, ∞) 182) f(x) = 182) _____ A) Decreasing: Increasing: , , B) Decreasing: (0, -3] Increasing: [-3, ∞) C) Decreasing: (0, 1] Increasing: [1, ∞) D) Decreasing: (0, ∞) 183) f(x) = -4 – ln x 183) _____ A) Decreasing: (0, ∞) B) Increasing (-4, ∞) C) Increasing (0, ∞) D) Decreasing: (0, ∞) 184) f(x) = 2 – ln(x + 4) 184) _____ A) Decreasing: (4, ∞) B) Decreasing: (-4, ∞) C) Decreasing: (0, ∞) D) Decreasing: (-4, ∞) Solve the problem. 185) If $1250 is invested at a rate of 8 % compounded monthly, what is the balance after 10 years? [A = ] 185) _____ A) $2844.31 B) $2281.25 C) $1031.25 D) $1594.31 186) If $4,000 is invested at 7% compounded annually, how long will it take for it to grow to $6,000, assuming no withdrawals are made? Compute answer to the next higher year if not exact. [A = A) 6 years ] 186) _____ B) 2 years C) 8 years D) 5 years 187) In North America, coyotes are one of the few species with an expanding range. The future population of coyotes in a region of Mississippi valley can be modeled by the equation , where t is time in years. Use the equation to determine when the population will reach 170. (Round your answer to the nearest tenth year.) 187) _____ A) 583.1 years B) 581.3 years C) 586.2 years D) 578.0 years 188) A country has a population growth rate of 2.4% compounded continuously. At this rate, how long will it take for the population of the country to double? Round your answer to the nearest tenth. 188) _____ A) 30 years B) 2.9 years C) .29 years D) 28.9 years 189) A carbon-14 dating test is performed on a fossil bone, and analysis finds that 15.5% of the original amount of carbon-14 is still present in the bone. Estimate the age of the fossil bone. (Recall that carbon-14 decays according to the equation A = ). A) 15, 000 years B) 1,500 years 189) _____ C) 150 years D) 15,035 years 190) Assume that a savings account earns interest at the rate of 2% compounded monthly. If this account contains $1000 now, how many months will it take for this amount to double if no withdrawals are made? 190) _____ A) 408 months B) 417 months C) 12 months D) 450 months 191) U. S. Census Bureau data shows that the number of families in the United States (in millions) in year x is given by h(x) = 51.42 + 15.473 ∙ log x , where x = 0 is 1980. How many families were there in 2002? 191) _____ A) 72 million B) 48 million C) 90 million D) 21 million 192) The level of a sound in decibels (db) is determined by the formula N = 10 ∙ log(I × ) db, where I is the intensity of the sound in watts per square meter. A certain noise has an intensity of sound level of this noise? (Round your answer to the nearest decibel.) per square meter. What is the A) 206 db B) 79 db 192) _____ C) 9 db D) 89 db 193) Book sales on the Internet (in billions of dollars) in year x are approximated by f(x) = 1.84 + 2.1 ∙ ln x, where x = 0 corresponds to 2000. How much will be spent on Internet book sales in 2008? Round to the nearest tenth. 193) _____ A) 3.9 billion B) 6.0 billion C) 6.2 billion D) 8.0 billion 1) D 2) B 3) B 4) A 5) B 6) B 7) C 8) C 9) A 10) A 11) C 12) B 13) B 14) B 15) B 16) B 17) B 18) D 19) -27, -12, 20) 53 21) -5 22) B 23) C 24) B 25) A 26) D 27) f(x) = has domain all real numbers except x = 48. 28) B 29) A 30) A 31) A 32) B 33) B 34) C 35) B 36) A 37) A 38) B 39) A 40) D 41) Choice (A) defines a function. To each element (student) of the first set (or domain), there corresponds exactly one element (teacher) of the second set (or range). Choice (B) does not define a function. An element (student) of the first set (or domain) corresponds to more that one element (teacher) of the second set (or range). 42) C 43) A 44) C 45) D 46) A 47) D 48) A 49) D 50) B 51) Basic function is f(x) = ; shift right 2 units, shift up 5 units. f(x) = +5 52) Basic function is f(x) = 53) D 54) C 55) D ; reflect over the x -axis, shift left 4 units, shift down 2 units. 56) g(x) = 57) C 58) B 59) D 60) C 61) C 62) A 63) C 64) C 65) D 66) D 67) B 68) B 69) A 70) B 71) C 72) B 73) D 74) f(x) = 0). 75) Max f(x) = 76) A 77) C 78) C 79) D 80) C 81) B 82) D 83) B + 9 ; vertex: (-2, 9); maximum: f(-2) = 9; Range of f = {y }; x-intercepts: (-5, 0), (1, 84) C 85) D 86) C 87) D 88) D 89) D 90) D 91) A 92) A 93) C 94) B 95) A 96) D 97) P(x) = 98) (A) (B) + 80.3x – 150, must sell approximately 6.69 million cameras. (x) = (C) 39; $182.46 99) B 100) A 101) B 102) B 103) A 104) B 105) A 106) C 107) B 108) C 109) A 110) A 111) B 112) B 113) A 114) D 115) B 116) D 117) D 118) D 119) C + 105 + x 120) C 121) C 122) C 123) D 124) D 125) B 126) D 127) B 128) D 129) B 130) B 131) B 132) C 133) B 134) C 135) A 136) B 137) B 138) B 139) D 140) y = 1.1389( 141) C 142) C 143) D 144) B 145) A 146) C 147) D 148) C 149) D 150) 2,018 bacteria 151) D 152) A 153) B 154) A 155) C 156) A 157) B 158) A 159) C 160) B 161) C 162) D 163) C 164) B 165) D 166) A 167) D 168) C 169) A 170) D 171) D ); $7.54; $9.30 172) D 173) D 174) A 175) D 176) C 177) A 178) B 179) A 180) C 181) A 182) C 183) A 184) B 185) A 186) A 187) D 188) D 189) D 190) B 191) A 192) D 193) C