MATH 1040 CP 11 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.

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1 MATH 1040 CP 11 SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Write the equation in its equivalent exponential form. 1) log = 3 1) 2) log 2 16 = x 2) Write the equation in its equivalent logarithmic form. 3) = 5 3) 4) 4 x = 64 4) Evaluate the expression without using a calculator. 5) log 2 1 5) 6) log ) 7) log ) Graph the function. 8) Use the graph of log 2 x to obtain the graph of f(x) = 2 log 2 x. 8) Graph the functions in the same rectangular coordinate system. 9) f(x) = 4 x and g(x) =log 4 x 9) Graph the function. 10) Use the graph of f(x) = log x to obtain the graph of g(x) = 4 - log x. 10) Find the domain of the logarithmic function. 11) f(x) = log 6 (x + 1) 2 11) 12) f(x) = log x + 5 x ) 13) f(x) = ln 1 x ) Evaluate the expression without using a calculator. 14) e ln 8x4 14) 1

2 Evaluate or simplify the expression without using a calculator. 15) ln 4 e 15) 16) 10 log 6 x 16) 17) 7 10 log ) Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. 18) ln e ) 19) ln 6 x 19) 20) log 2 x - 2 x 6 20) 21) log 4 10x 21) 22) log 2x x 3(x + 1) 2 22) 23) log 5 4 x 3 y z 2 23) 24) log 3 81 x ) Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. 25) 1 6 (log 6 x + log6 y) - 2 log6 (x + 3) 25) 26) 1 5 [5ln (x + 9) - ln x - ln (x2-9)] 26) Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. 4 27) log 2 27) x 2

3 Use properties of logarithms to condense the logarithmic expression. Write the expression as a single logarithm whose coefficient is 1. Where possible, evaluate logarithmic expressions. 28) log x + log (x 2-81) - log 6 - log (x - 9) 28) Use common logarithms or natural logarithms and a calculator to evaluate to four decimal places 29) log 26 29) Solve the equation by expressing each side as a power of the same base and then equating exponents. 30) 2 (7-3x) = ) 31) 25 x = ) Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 32) e 2x + e x - 6 = 0 32) 33) e x + 6 = 4 33) Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. 34) ln 6 + ln (x - 1) = 0 34) Solve the equation by expressing each side as a power of the same base and then equating exponents. 35) 16 x + 8 = 64 x ) Solve the logarithmic equation. Be sure to reject any value that is not in the domain of the original logarithmic expressions. Give the exact answer. 36) log 3 (x + 6) + log 3 (x - 6) - log 3 x = 2 36) 37) log 5 (x + 2) = -3 37) 38) ln (x - 6) + ln (x + 1) = ln (x - 15) 38) 39) log (x + 24) - log 4 = log (10x + 4) 39) 40) ln (x - 3) - ln (x + 8) = ln (x - 6) - ln (x + 8) 40) Solve the problem. 41) The formula A = 238e 0.032t models the population of a particular city, in thousands, t years after When will the population of the city reach 317 thousand? 41) 3

4 360 42) The logistic growth function f(t) = describes the population of a species of e-0.15t butterflies t months after they are introduced to a non-threatening habitat. What is the limiting size of the butterfly population that the habitat will sustain? 42) Solve. 43) A fossilized leaf contains 13% of its normal amount of carbon 14. How old is the fossil (to the nearest year)? Use 5600 years as the half-life of carbon ) 44) The half-life of silicon-32 is 710 years. If 60 grams is present now, how much will be present in 800 years? (Round your answer to three decimal places.) 44) 45) The value of a particular investment follows a pattern of exponential growth. In the year 2000, you invested money in a money market account. The value of your investment t years after 2000 is given by the exponential growth model A = 8300e 0.064t. How much did you initially invest in the account? 45) Use Newton's Law of Cooling, T = C + (T0 - C)e kt, to solve the problem 46) A cup of coffee with temperature 101 F is placed in a freezer with temperature 0 F. After 6 minutes, the temperature of the coffee is 61.4 F. What will its temperature be 17 minutes after it is placed in the freezer? Round your answer to the nearest degree. 46) Present data in the form of tables. For the data set shown by the table, a. Create a scatter plot for the data. b. Use the scatter plot to determine whether an exponential function or a logarithmic function is the best choice for modeling the data. 47) Number of Homes Built in a Town by Year Year Number of Homes ) 4

5 Answer Key Testname: MATH1040CP11 1) 5 3 = 125 2) 2 x = 16 3) log = 1 3 4) log 4 64 = x 5) 0 6) -1 7) 10 8) 9) 10) 11) (-, -1) or (-1, ) 12) (-, -5) (2, ) 5

6 Answer Key Testname: MATH1040CP11 13) (-5, ) 14) 8x 4 15) ) x 1/6 17) ) 4 - ln 5 19) 1 6 ln x 20) log 2 (x - 2) - 6 log 2 x 21) 1 2 log log 4 x 22) log 2 + 5log x + 1 log (1 - x) - log 3-2log (x + 1) 3 23) 1 4 log 5 x log 5 y - 2 log 5 z 24) log 3 (x - 1) 25) log6 6 xy (x + 3) 2 5 (x + 9)5 26) ln x(x 2-9) 27) 2 - log 2 x 28) log 29) ) {3} 31) ) ) ) { 7 6 } 35) {22} 36) {12} 37) ) 8 39) 39 x(x + 9) 6 40) ) ) 360 butterflies 43) 16,453 6

7 Answer Key Testname: MATH1040CP11 44) ) $ ) 25 F 47) a. b. Exponential function 7

nt and A = Pe rt to solve. 3) Find the accumulated value of an investment of $10,000 at 4% compounded semiannually for 5 years.

Exam 4 Review Approximate the number using a calculator. Round your answer to three decimal places. 1) 2 1.7 2) e -1.4 Use the compound interest formulas A = P 1 + r n nt and A = Pe rt to solve. 3) Find