Exam Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. You are planning on purchasing a new car and have your eye on a specific model. You know that new car prices are projected to increase at a rate of 5% per year for the next few years. 1) Write an equation that represents the projected cost C, of your dream car t years in the 1) future, given that it costs $28,000 today. Use your equation to project the cost of you car 5 years from now. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the equation that matches the given graph. 2) 2) A) h(x) = 0.3x B) h(x) = -2.8(1.8)x C) h(x) = 2.8(0.3)x D) h(x) = 2.8(1.6)x SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Complete the following table representing an exponential function. Round calculations to two decimal places whenever necessary. 3) x 0 1 2 3 4 3) y 4.00 9.12 The given table represents an exponential function. Use it to write a symbolic rule for the function. 4) x 0 1 y 3.0 7.2 4) 1
Without graphing, classify the function as increasing or decreasing, and determine f(0). 5) f(x) = 1.8(0.30)x 5) Graph the function. 6) f(x) = 4x 6) Solve the problem. 7) Your starting salary for a new job is $33,000 per year. You are offered two options for salary increases: 7) Plan 1: an annual increase of $1000 per year or Plan 2: an annual increase of 3% per year Your salary is a function of the number of years of employment at your job. Write an equation to determine the salary, S, after x years on the job using plan 1; using plan 2. 8) The number of books in a small library increases according to the function B = 8500e0.05t, where t is measured in years. How many books will the library have after 5 years? 8) Write in logarithmic form. 9) 73 = 343 9) 2
Write in exponential form. 1 10) log = -2 10) 3 9 11) log 3 9 = 2 11) Write in logarithmic form. 12) 5-2 = 1 25 12) Solve the problem. 13) The amount of money given in grants by a foundation is displayed in the table. 13) Annual Giving Year (in millions of dollars) 1990 8.1 1992 9.9 1994 12.1 1996 14.6 1998 18.7 1999 21.5 Let f(t) represent the amount of giving (in millions of dollars) by the foundation for the year that is t years since 1990. Find an exponential model f(t) = abt using the data for 1992 and 1996. 14) Suppose that an investment of $12,000 grows in value at a rate of 7% per year. What is the growth factor for this investment? 14) 3
15) Suppose that an investment of $13,000 grows in value at a rate of 5% per year. By what factor has the value increased at the end of t years? 15) 16) The table below shows the number of subscribers to a certain magazine in various years. Use regression to fit an exponential function N(t) = abt to the data where t is the number of years since 1980 and N is the number of subscribers in thousands. Round regression coefficients to four decimal places. 16) Year Subscribers (thousands) 1980 3.4 1983 7.8 1988 12.9 1992 25.6 1997 48.0 Without graphing, classify the function as increasing or decreasing, and determine f(0). 17) f(x) = 0.3(1.01)x 17) Solve the equation for the unknown variable. 18) log 3 27 = x 18) Write the expression as a sum, difference, or multiple of logarithms. 19) log 4 x4y6 z 5 w6 19) Rewrite the expression as the logarithm of a single quantity. 20) 4 log 4 (4x + 4) + 3 log 4 (5x + 2) 20) 4
Use the change of base formula and your calculator to approximate the logarithm. 21) log 7 23 21) Solve the equation. Round your answer to four decimal places. 22) 3.5 log 3 (x - 1) = 6 22) Solve the problem. 23) The following table shows per capita health care expenditures (in dollars) from 1995 to 2000. 23) Year 1995 1996 1997 1998 1999 2000 Expenditure ($) 3028 3581 3902 4095 4283 4417 The logarithmic model that fits this data is E = f(x) = 3130 + 720 ln x, where E represents the per capita health care expenditures and x is the number of years since 1994. Use this model to predict the per capita health care expenditures in 2006. Solve the equation. Round your answer to four decimal places. 24) log 3 13 + log 3 (x - 1) = 7 24) 25) 3 4 x = 5 x 25) 26) 2.5 2 2x + 1 = 3 1.5 x - 1 26) Use the change of base formula and your calculator to approximate the logarithm. 27) log 248.0 27) 4 5
28) log 7 31 28) Rewrite the expression as the logarithm of a single quantity. 29) 1 4 log x - 1 2 log y - 5 4 log z 29) Write the expression as a sum, difference, or multiple of logarithms. 30) log 5 x4 y8 5 30) 31) log b x8y7 z9 31) Solve the equation for the unknown variable. 32) log 2 26 = a 32) 33) log y 625 81 = 4 33) 6