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Name: _____________________________ Class: _____________ Date: __________ Exponentials/Logs Multiple Choice Post-Test Multiple Choice Identify the choice that best completes the statement or answers the question. ____ 1 Graph y = log(x + 1) − 7 A B C D ____ 2 The pH of a liquid is a measure of how acidic or basic it is. The concentration of hydrogen ions in a ÈÍ ˘˙ liquid is labeled ÍÍÍ H + ˙˙˙ . Use the formula pH = −log [H + ] to answer questions about pH. Î ˚ Find the pH level, to the nearest tenth, of a liquid with [H+] about 6.5x 10 −3 . A 3.8 B 2.2 ____ ____ C -3.8 D 3.0 3 Write the logarithmic expression as a single logarithm: 5 log b q + 2 log b y A log b (q 5 y 2 ) C log b (q 5 + y 2 ) B D log b ÊÁÁ qy 5 + 2 ˆ˜˜ (5 + 2) log b (q + y) 4 Expand the logarithmic expression: log 7 A −x log7 2 B log 7 x log 7 2 Ë ¯ x 2 C log 7 2 − log 7 x D log 7 x − log 7 2 ____ 5 Use the properties of logarithms to evaluate log 3 9 + log 3 36 − log 3 4. A 2 C 8 B 4 D 41 ____ 6 Use a graphing calculator. Solve 5 4x = 2115 by graphing. Round to the nearest hundredth. A 1.19 B 0.83 Algebra II Exponentials Post-Test C 8 D 41 Page 2 ____ 7 Use the Change of Base Formula to solve 2 2x = 90. Round to the nearest ten-thousandth. A 7.6133 B 9.3658 ____ C 3.2459 D 12.9837 8 Which value of x satisfies the equation 2(5 x ) = 250? A 1 B 2 ____ C 3 D 4 9 The half-life of Carbon-14 is about 5730 years. It was determined that a bone specimen contained about 35% of Carbon-14. Which type of function models the number of years ago that this animal was alive? A Linear B Quadratic ____ 10 Identify the logarithmic form of 10 0.602 = 4 A log 10 0.602 = B ____ C Exponential D Logarithmic log 10 1 4 1 = 0.602 4 C log 10 4 = −0.602 D log 10 4 = 0.602 11 Which of the following represents a shift of 5 units left and 6 units down from the graph of f(x) = log x? A g(x) = log(x + 5) − 6 B g(x) = log(x + 5) + 6 ____ C g(x) = log(x − 5) − 6 D g(x) = log(x − 5) + 6 12 Solve log(4x + 10) = 3. 7 4 247.5 A − C 250 B D 990 Algebra II Exponentials Post-Test Page 3 ____ ____ 13 What is the inverse of the function y = log 2 (x + 5)? A y = 2x C y = 2x + 5 B y = log −2 (x − 5) D y = 2x − 5 14 The amount of money in an account with continuously compounded interest is given by the formula A = Pe rt , where P is the principal, r is the annual interest rate, and t is the time in years. Calculate to the nearest hundredth of a year how long it takes for an amount of money to double if interest is compounded continuously at 6.2%. Round to the nearest tenth. A 1.1 yr B 6.9 yr ____ 15 Solve 15 2x = 36. Round to the nearest ten-thousandth. A 0.6616 B 2.6466 ____ C 11.2 yr D 0.6 yr C 1.7509 D 1.9091 16 Determine what family of functions models the graph below, then write a function for the graph. A exponential, y = 0.5(2) x B exponential, y = 2(0.5) x Algebra II Exponentials Post-Test C exponential, y = (2 ⋅ 0.5) x D logarithmic, y = 2(5) x Page 4 ____ ÊÁ 1 ˆ˜ x 17 Determine which of the following is a graph of y = 7 ÁÁÁÁ ˜˜˜˜ , then state the asymptote. Ë 4¯ A C asymptote: x = 0 B D asymptote: x = –4 ____ asymptote: x = 7 asymptote: x = 0 18 Find the annual percent increase or decrease that y = 0.35(2.3) x models. A 230% increase B 130% increase Algebra II Exponentials Post-Test C 30% decrease D 65% decrease Page 5 ____ 19 For an annual rate of change of –31%, find the corresponding growth or decay factor. A 0.31 B 0.69 ____ C 1.31 D 1.69 20 How much money invested at 5% compounded continuously for 3 years will yield $820? A $952.70 B $818.84 ____ C $780.01 D $705.78 21 Suppose you invest $1600 at an annual interest rate of 4.6% compounded continuously. How much will you have in the account after 4 years? A $800.26 B $6,701.28 ____ C $10,138.07 D $1,923.23 22 The half-life of a certain radioactive material is 85 days. An initial amount of the material has a mass of 801 kg. Write an exponential function that models the decay of this material. Find how much radioactive material remains after 10 days. Round your answer to the nearest thousandth. 1 ____ A x 1 ÊÁ 1 ˜˜˜ˆ 85 y = ÁÁÁÁ ; 0.228 kg 2 Ë 801 ˜˜¯ B ÊÁ 1 ˜ˆ 85 x y = 801 ÁÁÁÁ ˜˜˜˜ ; 0 kg Ë 2¯ 1 C ÊÁ 1 ˜ˆ 85 x y = 801ÁÁÁÁ ˜˜˜˜ ; 738.273kg Ë 2¯ D ÊÁ 1 ˜ˆ 85 x ˜˜ y = 2 ÁÁÁÁ ; 0.911 kg ˜ Ë 801 ˜¯ 1 23 What is the inverse of the function: f(x) = 4 x − 4? A B f −1 (x) = 4 −x + 4 −1 1 x f (x) = 4 + 4 Algebra II Exponentials Post-Test C f −1 (x) = log 4 (x + 4) D f −1 (x) = log(x + 4) Page 6 ____ 24 Graph y = 7 (6) A x+2 B ____ + 1. C D 25 Evaluate log 0.01 A –10 B –2 Algebra II Exponentials Post-Test C 2 D 10 Page 7 ____ 26 Write the equation log 32 8 = 3 in exponential form. 5 3 A 32 5 = 8 C ÊÁ 3 ˜ˆ 32 ÁÁ ˜˜ = 8 ÁÁ 5 ˜˜ Ë ¯ 3 B ____ ____ 8 5 5 = 32 27 Evaluate log 3 81 A 4 B -4 D 8 3 = 32 C 3 D 2 28 Decibels (dB) are defined by the equation; 10log I , where I o = 10−12 , the intensity of a barely audible Io sound. Use the formula to determine the loudness in dB of a busy street, which measures an intensity of 10−5 . A 10 dB B 70 dB ____ 29 Write an exponential function y = ab x for a graph that includes (1, 15) and (0, 6). A B ____ C -17 dB D 7 dB y = 6(2.5) x y = 2(5) x C D y = 2.5(6) x y = 6(2) x 30 An initial population of 725 quail increases at an annual rate of 5%. Write an exponential function to model the quail population. A B f(x) = 725(.05) x f(x) = 725(1.05) x Algebra II Exponentials Post-Test C D f(x) = 725(5) x f(x) = (725 ⋅ 0.05) x Page 8 ____ 1 2 31 Rewrite in logarithmic form ( ) x = y 1 2 A x = logy C log 1 y = x 2 B log x = y 1 2 D log 1 x = y 2 ____ 2 3 32 Solve the equation (x − 7) = 4 A 11 B 1; -1 ____ C -3 D 15; -1 33 If there are initially 1500 bacteria in a culture, and the number of bacteria double each hour, the number of bacteria after t hours can be found using the formula N = 1500(2 t ). How long will it take the culture to grow to 50,000 bacteria? A 5.06 hr B 24.25 hr Algebra II Exponentials Post-Test C 3.04 hr D 1.52 hr Page 9