MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.

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1 Exam Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Decide if the function is an exponential function. If it is, state the initial value and the base. 1) y = - 8 4x A) Exponential Function; base = - 32; initial value = 1 B) Exponential Function; base = 4; initial value = - 8 C)Exponential Function; base = x; initial value = - 8 D) Not an exponential function 1) 2) y = x8.8 A) Exponential Function; base = x; initial value = 0 B) Exponential Function; base = x; initial value = 1 C) Not an exponential function D) Exponential Function; base = 8.8; initial value = 0 2) Compute the exact value of the function for the given x-value without using a calculator. 3) f(x) = 1 5 x for x = 3 3) A) B) 125 C) D) 1 15 Determine a formula for the exponential function. 4) The graph of an exponential function is given. Which of the following is the correct equation of the function? 4) 10 y x A) y = 2.4x B) y = 0.65x C)y = 3.5x D) y = 0.32x 1

2 State whether the function is an exponential growth function or exponential decay function, and describe its end behavior using limits. 5) f(x) = e3x 5) A) Exponential growth function; lim f(x) = 0; lim f(x) = B) Exponential decay function; lim f(x) = ; lim f(x) = 0 C) Exponential growth function; lim f(x) = ; lim f(x) = 0 D) Exponential decay function; lim f(x) = 0; lim f(x) = 6) In September 1998 the population of the country of West Goma in millions was modeled by f(x) = 17.7e0.0018x. At the same time the population of East Goma in millions was modeled by g(x) = 13.9e0.0186x. In both formulas x is the year, where x = 0 corresponds to September Assuming these trends continue, estimate the year when the population of West Goma will equal the population of East Goma. A) 2010 B) 1984 C) 14 D) ) Suppose the amount of a radioactive element remaining in a sample of 100 milligrams after x years can be described by A(x) = 100e x. How much is remaining after 103 years? Round the answer to the nearest hundredth of a milligram. A) milligrams B) 0.31 milligrams C) milligrams D) milligrams 6) 7) Solve the equation. 8) (1/4)x = 256 A) -4 B) -1/4 C)4 D) 1/4 8) 9) 3(10-2x) = 81 A) 3 B) 5 C)27 D) -3 9) Decide whether the function is an exponential growth or exponential decay function and find the constant percentage rate of growth or decay. 10) f(x) = x 10) A) Exponential growth function; 108% B) Exponential growth function; 0.08% C) Exponential growth function; 8% D) Exponential decay function; 108% Find the exponential function that satisfies the given conditions. 11) Initial value = 68, decreasing at a rate of 0.48% per week A) f(t) = t B) f(t) = t C)f(t) = t D) f(t) = t 11) 12) Initial population = 1092, doubling every 7 hours A) P(t) = t B) P(t) = t/7 12) C)P(t) = 7 2t D) P(t) = t/7 2

3 Find the logistic function that satisfies the given conditions. 13) Initial height = 169, limit to growth = 845, passing through (2, 585) A) f(x) = B) f(x) = 1 + 4(1/9x 1 + 2(1/3)x C)f(x) = (1/3)x D) f(x) = (1/3)x 13) 14) The number of books in a small library increases according to the function B = 3400e0.02t, where t is measured in years. How many books will the library have after 10 years? A) 2376 B) 5472 C) 5389 D) ) There are currently 73 million cars in a certain country, increasing by 1.7% annually. How many years will it take for this country to have 91 million cars? Round to the nearest year. A) 11 yr B) 4 yr C)170 yr D) 13 yr 14) 15) 16) The number of students infected with the flu on a college campus after t days is modeled by the 320 function P(t) =. What was the initial number of infected students? e-0.3t A) 8 B) 16 C)320 D) 39 17) The number of students infected with the flu on a college campus after t days is modeled by the 240 function P(t) =. What is the maximum number of infected students possible? e-0.3t A) 240 B) 6 C)120 D) ) 17) Evaluate the logarithm. without using a calculator 18) log 8 ( 1 8 ) 18) A) 0 B) 8 C)1 D) -1 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Simplify the expression. 19) eln 20 19) 20) 10log ) MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Solve the equation by changing it to exponential form. 21) log 5 x = -4 21) A) x = -5 4 B) x = 1 54 C)x = - 4 log54 D) x = - (4)5 3

4 Describe how to transform the graph of the basic function g(x) into the graph of the given function f(x). 22) f(x) = ln (x + 7) - 9; g(x) = ln x A) Translate 7 units to the left and 9 units up. B) Translate 9 units to the left and 7 units up. C)Translate 7 units to the left and 9 units down. D) Translate 7 units to the right and 9 units down. 22) 23) Wind speed varies in the first twenty meters above the ground. For a particular day, let f(x) = 1.7ln x compute the wind speed x meters above the ground. What is the wind speed 12 meters above the ground? Round results to the nearest hundredth. A) meters per second B) meters per second C) meters per second D) meters per second 23) Rewrite the expression as a sum or difference or multiple of logarithms. 24) log s2r 24) A) 1 5 log log13 s - log13 r B) log log13 s - log13 r C) 1 5 log log13 s - 2 log13 r D) 5 log log13 s - log13 5 Use the product, quotient, and power rules of logarithms to rewrite the expression as a single logarithm. Assume that all variables represent positive real numbers. 25) 5 log4 (3x - 3) + 3 log4 (5x + 6) 25) A) log4 (3x - 3) 5 (5x + 6)3 B) log4 ((3x - 3)5 + (5x + 6)3) C)15 log4 (3x - 3)(5x + 6) D) log4 (3x - 3)5(5x + 6)3 Use the change of base rule to find the logarithm to four decimal places. 26) log A) B) C) D) ) 27) An earthquake was recorded which was 316,228 times more powerful than a reference level zero earthquake. What is the magnitude of this earthquake on the Richter scale? Intensity on the Richter scale is log10(i/io). A) 5.5 B) 4.5 C) 12.7 D) ) Use the formula D = 10.0 log (S/So), where D is loudness of the sound in decibels, S is the intensity of the sound (watt/m2) produced by the sound wave, and So = 1.00 x watt/m2. What is the intensity in watt/m2 of a noise measured at 78 decibels? (Round to the nearest tenth.) A) 6.3 x 10-4 watt/m2 B) 2.4 x 1015 watt/m2 C)6.3 x 10-5 watt/m2 D) 7.8 x watt/m2 27) 28) 4

5 Find the exact solution to the equation. 29) log4(x - 2) = - 1 A) x = B) x =6 C)x = 2 D) x = ) 30) 3(12-2x) = 81 A) x = 4 B) x = -4 C)x = 6 D) x = 27 30) Use a calculator to find an approximate solution to the equation. 31) e-t = 0.03 A) B) C) D) ) 32) (3.4)x = 43 A) B) C) D) ) Solve the equation. 33) ex + e-x = 3 A) , B) 0.557, C) , D) , ) 34) log 3x = log 5 + log (x - 2) 34) A) B) 3 2 C) 5 D) -5 35) e-0.3t = 275 A) B) C) D) ) 36) By how many orders of magnitude do two earthquakes differ if one is rated 4.3 on the Richter scale and the other is rated 6.7? A) 1.9 B) 1.2 C)4.8 D) ) 37) A cake is removed from an oven at 325 F and cools to 150 F after 25 minutes in a room 68 F. How long will it take the cake to cool to 113 F? A) 38.1 min B) min C)22.86 min D) min 37) Find the amount accumulated after investing a principal P for t years at an interest rate r. 38) P = $14,000, t = 9, r = 12%, compounded semiannually (k = 2) A) $37, B) $25, C) $39, D) $38, ) 39) P = $840, t = 5, r = 1% compounded continuously A) $124, B) $ C) $ D) $ ) 40) Find the future value accumulated in an annuity after investing periodic payments of $450 for 9 years at an annual interest rate of 5%, with payments made and credited 4 times per year. A) $12, B) $36, C) $24, D) $20, ) 5

6 41) Find the periodic payment of a loan with present value $1800 and an annual interest rate 8% for a term of 4 years, with payments made and interest charged 12 times per year. A) $43.94 B) $79.10 C) $87.89 D) $ ) 42) How long will it take for prices in the economy to double at a 4% annual inflation rate? (Round to the nearest year.) A) 14 yr B) 18 yr C)23 yr D) 28 yr 42) 43) How long will it take for $3600 to grow to $40,200 at an interest rate of 12.1% if the interest is compounded quarterly? Round the number of years to the nearest hundredth. A) B) C) D) ) Determine the doubling time of the investment. 44) $1400 at 6% compounded quarterly A) years B) years C) years D) 9.31 years 44) 45) 5.08% APR compounded continuously A) years B) years C) years D) years 45) 46) Find the annual percentage yield if the interest rate is 3.0% and interest is compounded quarterly. A) 3.28% B) 3.53% C) 3.03% D) 2.78% 46) 47) Find the annual percentage yield if the interest rate is 6.0% and interest is compounded daily (n = 365). A) 6.43% B) 5.93% C) 6.68% D) 6.18% 47) 6