from file exam.pdf, only questions from 20 to 40.
IMG_3848.jpg IMG_3849.jpg IMG_3850.jpg MATH 146 - 4, 5, 6 exam study guide Name___________________________________ 1) Rewrite as a single logarithm: 7 ln x - 1 3 ln y 1) A) ln x7y3 B) ln x 7 3 y C) ln x 7 y3 D) ln x7 3 y 2) Rewrite as a single logarithm: ln x + 8ln y 2) A) ln (x + 8y) B) ln x y8 C) ln xy8 D) ln 8xy Begin by graphing the standard function f(x) = x3 Then use transformations of this graph to graph the given function. 3) g(x) = x3 + 3 3) A) B) C) D) 1 Begin by graphing the standard quadratic function f(x) = x2 . Then use transformations of this graph to graph the given function. 4) h(x) = (x - 2)2 4) A) B) C) D) 2 Begin by graphing the standard square root function f(x) = x . Then use transformations of this graph to graph the given function. 5) g(x) = -x - 1 5) A) B) C) D) 3 6) g(x) = x - 1 6) A) B) C) D) Evaluate or simplify the expression without using a calculator. 7) ln e3 7) A) 3 B) 1 3 C) 1 D) e 8) 10log 6 x 8) A) x-1/6 B) 6 C) x1/6 D) x6 9) 6 10 log 4.4 9) A) 264 B) 2.64 C) 8.8896 D) 26.4 4 Evaluate the expression without using a calculator. 10) eln 242 10) A) e242 B) ln 242 C) 242 D) -242 11) log 9 9 11) A) 9 B) 0 C) 1 9 D) 1 Find the domain of the logarithmic function. 12) f(x) = ln (4 - x) 12) A) (- , 0) B) (-4, ) C) (- , 4) D) (- , 4) or (4, ) Begin by graphing the standard absolute value function f(x) = x . Then use transformations of this graph to graph the given function. 13) h(x) = - x + 2 13) A) B) C) D) 5 Begin by graphing the standard cubic function f(x) = x3. Then use transformations of this graph to graph the given function. 14) g(x) = - 1 4 x3 14) A) B) C) D) 6 15) g(x) = -x3 - 2 15) A) B) C) D) 7 Graph the function by making a table of coordinates. 16) f(x) = 5x 16) A) B) C) D) Rewrite the equation in terms of base e. Express the answer in terms of a natural logarithm, and then round to three decimal places. 17) y = 4(1.7)x 17) A) y = 4ex ln 1.7, y = 4e0.531x B) y = 1.7ex ln 4, y = 1.7e1.386x C) y = (ln 4)ex ln 1.7, y = 1.386e0.531x D) y = 4e1.7x, y = 42.7180.531x 8 Solve the equation by expressing each side as a power of the same base and then equating exponents. 18) 3(3x - 6) = 27 18) A) {9} B) {3} C) {1 9 } D) {-3} Solve the exponential equation. Use a calculator to obtain a decimal approximation, correct to two decimal places, for the solution. 19) 9ex = 25 19) A) 2.3 B) -1.02 C) 0.44 D) 1.02 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. 20) 2log x = log 36 20) A) {±6} B) {6} C) 3 D) {-6} 21) ln x + 7 = 7 21) A) {e7 - 7} B) {e14 + 7} C) e 7 2 + 7 D) {e14 - 7} 22) ln x = 2 22) A) {ln 2} B) 2e C) 2 ln 1 D) e2 Solve the problem. 23) The population of a particular country was 23 million in 1984; in 1992, it was 32 million. The exponential growth function A =23ekt describes the population of this country t years after 1984. Use the fact that 8 years after 1984 the population increased by 9 million to find k to three decimal places. 23) A) 0.041 B) 0.275 C) 0.051 D) 0.825 24) The formula A = 106e0.032t models the population of a particular city, in thousands, t years after 1998. When will the population of the city reach 120 thousand? 24) A) 2003 B) 2002 C) 2004 D) 2005 25) The function D(h) = 5e-0.4h can be used to determine the milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. How many milligrams (to two decimals) will be present after 11 hours? 25) A) 407.25 mg B) 1.49 mg C) 3.09 mg D) 0.06 mg 26) The population in a particular country is growing at the rate of 2.8% per year. If 2,546,000 people lived there in 1999, how many will there be in the year 2004? Use f(x) =ae0.028t and round to the nearest ten-thousand. 26) A) 2,930,000 B) 3,220,000 C) 3,510,000 D) 2,870,000 9 27) A city is growing at the rate of 0.6% annually. If there were 4,840,000 residents in the city in 1993, find how many (to the nearest ten-thousand) are living in that city in 2000. Use y = 4,840,000(2.7)0.006t. 27) A) 5,050,000 B) 13,070,000 C) 550,000 D) 5,080,000 Solve. 28) 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 = 3300e0.053t. How much did you initially invest in the account? 28) A) $3300.00 B) $3479.62 C) $1650.00 D) $174.90 Use properties of logarithms to expand the logarithmic expression as much as possible. Where possible, evaluate logarithmic expressions without using a calculator. 29) ln x y 29) A) 1 2 ln x - 1 2 ln y B) 1 2 ln x - ln y C) 1 2 ln x y D) ln x - ln y 30) ln 9 x 30) A) 9ln x B) 1 9 ln x C) x ln 9 D) 9ln x 31) ln e 5 9 31) A) ln e5 - ln 9 B) 5 - ln 9 C) 5 + ln 9 D) ln e5 + ln 9 32) log (10,000x) 32) A) 4x B) 40 + log x C) 4log x D) 4 + log x Use the compound interest formulas A = P 1 + r n nt and A = Pert to solve. 33) Suppose that you have $10,000 to invest. Which investment yields the greater return over 7 years: 8.75% compounded continuously or 8.9% compounded semiannually? 33) A) $10,000 invested at 8.9% compounded semiannually over 7 years yields the greater return. B) Both investment plans yield the same return. C) $10,000 invested at 8.75% compounded continuously over 7 years yields the greater return. 10 Use the graph of the function f, plotted with a solid line, to sketch the graph of the given function g. 34) g(x) = f(x - 2) y = f(x) 34) A) B) C) D) 11 35) g(x) = f(x) + 1 y = f(x) 35) A) B) C) D) Use the graph of y = f(x) to graph the given function g. 36) g(x) = 2f(x) 36) 12 A) B) C) D) Write the equation in its equivalent exponential form. 37) log b 9 = 2 37) A) 92 = b B) b2 = 9 C) 9b = 2 D) 2b = 9 Write the equation in its equivalent logarithmic form. 38) 63 = x 38) A) log 3 x = 6 B) log 6 3 = x C) log 6 x = 3 D) log x 6 = 3 For each 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, a logarithmic function, or a linear function is the best choice for modeling the data. 39) Number of Homes Built in a Town by Year Year Number of Homes 1985 10 1991 90 1994 145 1997 191 2002 223 39) 13 Answer Key Testname: 456 STUDY GUIDE 1) B 2) C 3) A 4) B 5) A 6) C 7) A 8) C 9) D 10) C 11) D 12) C 13) D 14) B 15) B 16) C 17) A 18) B 19) D 20) B 21) D 22) D 23) A 24) B 25) D 26) A 27) A 28) A 29) A 30) B 31) B 32) D 33) C 34) D 35) A 36) D 37) B 38) C 14 Answer Key Testname: 456 STUDY GUIDE 39) Exponential function 15