Name: Class: Date: Exponentials/Logs Multiple Choice Pre-Test

Transcription

1 Name: _ Class: _ Date: Eponentials/Logs Multiple Choice Pre-Test Multiple Choice Identify the choice that best completes the statement or answers the question. Graph y = log( + ) + 7 A C B D

2 2 The ph of a liquid is a measure of how acidic or basic it is. The concentration of hydrogen ions in a liquid È is labeled H + ÎÍ. Use the formula ph = log [ H + ] to answer questions about ph. Find the ph level, to the nearest tenth, of a liquid with [H + ] about A -2.5 C -.5 B 2.5 D.5 3 Write the logarithmic epression as a single logarithm: 2 log b q + 3 log b y A (2 + 3) log b (q + y) C log b (q 2 + y 3 ) B log b (q 2 y 3 ) D log b qy ˆ Á 4 Epand the logarithmic epression: log 4 3 A log 4 3 log 4 C log 4 log 4 3 B log 4 3 D log 4 3 log 4 5 Use the properties of logarithms to evaluate log log log 3 8. A 7 C 9 B D 5 6 Use a graphing calculator to solve 3 2 = 95 by graphing. Round to the nearest hundredth. A 5.22 C 2.40 B 2.6 D Use the Change of Base Formula to solve 5 4 = 25. Round to the nearest ten-thousandth. A C B.894 D Algebra II Eponentials Pre-Test Page 2

3 8 Which value of satisfies the equation 4(3 ) = 324? A C 3 B 2 D 4 9 The half-life of Carbon-4 is about 5730 years. It was determined that a bone specimen contained about 65% of Carbon-4. Which type of function models the number of years ago that this animal was alive? A Linear C Eponential B Quadratic D Trigonometric 0 Identify the logarithmic form of 3 5 = 243 A log 3 5 = C log = 5 B log = 5 D log243 = 5 Which of the following represents a shift of 5 units right and 6 units up from the graph of f() = log? A g() = log( + 5) 6 C g() = log( 5) 6 B g() = log( + 5) + 6 D g() = log( 5) Solve log(3 + 0) = 2. A 30 C 0 B 8 3 D 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 3.%. Round to the nearest tenth. A 2.2 yr C 22.4 yr B 3.8 yr D 5.5 yr Algebra II Eponentials Pre-Test Page 3

4 4 Solve 4 = 48. Round to the nearest ten-thousandth. A C.0909 B D State the family of functions the graph belongs to, then write a function to model the graph. A eponential, y = 4(0) C eponential, y = (0 4) B eponential, y = 0(4) D logarithmic, y = 2(0) Algebra II Eponentials Pre-Test Page 4

5 Ê 6 Choose the graph of y = 7 0 ˆ Á 4 and state the asymptote. A C B asymptote: = 0 D asymptote: = 7 asymptote: = 4 asymptote: = 0 7 Find the annual percent increase or decrease that y = 0.35(.65) models. A 65% increase C 35% decrease B 65% increase D 65% decrease Algebra II Eponentials Pre-Test Page 5

6 8 For an annual rate of change of +3%, find the corresponding growth or decay factor. A 0.3 C.3 B 0.69 D.69 9 How much money invested at 3% compounded monthly for 3 years will yield $520? A $48.78 C $ B $79.42 D $ What is the inverse of the function: f() = 3? A f () = 3 C f () = log 3 B f () = 3 D f () = log 2 Suppose you invest $200 at an annual interest rate of 2.3% compounded continuously. How much will you have in the account after 4 years? A $,2.08 C $2, B $,35.64 D $3, The half-life of a certain radioactive material is 85 days. An initial amount of the material has a mass of 80 kg. Write an eponential function that models the decay of this material. Find how much radioactive material remains after 0 days. Round your answer to the nearest thousandth. A y = Ê ˆ 85 Ê 2 Á 80 ; kg C y = 80 ˆ 85 Á 2 ; kg Ê B y = ˆ Ê ˆ 85 Á 2 ; 0 kg D y = 2 Á 80 ; 0.9 kg Algebra II Eponentials Pre-Test Page 6

7 Ê 23 Graph y = 7 ˆ Á 6 A C B D 24 Evaluate log 0. A 0 C B D 0 Algebra II Eponentials Pre-Test Page 7

8 25 Decibels (db) are defined by the equation; 0log I I o, where I o = 0 2, the intensity of a barely audible sound. Use the formula to determine the loudness in db of a jackhammer, which measures an intensity of 0 2. A 0 db C 20 db B 00 db D -0 db 26 What is the inverse of the function y = log( 4)? A y = 0 C y = 0 4 B y = log 0 ( + 4) D y = Write the equation log 4 28 = 7 in eponential form. 2 A 4 28 = 7 4 Ê 7ˆ C 2 Á 2 = 28 B = 4 D = Evaluate log 4 64 A 4 C 3 B -4 D 2 29 Write an eponential function y = ab for a graph that includes (, 2) and (0, 9). A y = (2.5) C y = 9( 4 3 ) B y = 9(2) D y = 2( 3 ) Algebra II Eponentials Pre-Test Page 8

9 30 An initial population of 650 quail increases at an annual rate of 2.5%. Write an eponential function to model the quail population. A f() = 650(2.5) C f() = 650(.025) B f() = 650(.025) D f() = ( ) 3 Rewrite in logarithmic form (25) = 5 A 5 = log25 C log = 25 5 B log 25 5 = D log 25 = 5 32 Solve the equation ( 5) 4 = 27 3 A 96 C 26.8 B 8 D If there are initially 2200 bacteria in a culture, and the number of bacteria triple each hour, the number of bacteria after t hours can be found using the formula y = 2200(3) t. How long will it take the culture to grow to 60,000 bacteria? A 5.06 hr C 3.0 hr B 4.25 hr D.52 hr Algebra II Eponentials Pre-Test Page 9