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1 Name: Online ECh5 Prep Date: Scientific Calc ONLY! 4. Sketch the graph of the function. A) 9. Sketch the graph of the function. B) Ans B Version 1 Page 1

2 _ 10. Use a graphing utility to determine which graph below is the graph of the function. E) Ans: E 11. Use the One-to-One Property to solve the following equation for x. 1 6x1 D) Use the One-to-One Property to solve the following equation for x. x 18 C) 7 Ans C : 1. Which investment option will pay the most interest? A) 9.6% compounded annually B) 9.4% compounded semiannually C) 9.% compounded quarterly D) 9.0% compounded continuously E) These investments all pay the same amount of interest. Version 1 Page

3 14. Let Q represent a mass of radioactive radium ( 6 Ra) (in grams), whose half-life is 1599 years. The quantity of radium present after t years is t / Q Determine the quantity present after 400 years. Round to the nearest hundredth of a gram. D).5 g Rewrite the logarithmic equation log 4 in exponential form. 16 C) Rewrite the exponential equation 1 in logarithmic form. 9 A) 1 log Evaluate the function f ( x) log4 x at x without using a calculator. 4 B) 1 1. Identify the x-intercept of the function y log4 x. B) Identify the vertical asymptote of the function f ( x) log( x ). C) x. Identify the the value of the function f( x) log. D) 1 Version 1 Page

4 4. Use a graphing utility to graph the function. B) 5. Write the logarithmic equation ln in exponential form. A) e 4 6. Write the exponential equation 1/ e in logarithmic form. D) ln Evaluate the function f ( x) ln x at x Round to decimal places. (You may use your calculator.) B) Evaluate the function x f ( x) ln e at x 4 without using a calculator. A) 0. Identify the x-intercept of the function f ( x) 4ln( x 1). D) x = Version 1 Page 4

5 1. Solve the equation ln x ln( e ) for x using the One-to-One Property. D) e. Solve the equation log(1 x) log(10) for x using the One-to-One Property. B) 9 5. Rewrite the logarithm log4 1 in terms of the natural logarithm. A) ln1 ln 4 6. Rewrite the logarithm log5 in terms of the common logarithm (base 10). B) log log5 9. Simplify the expression log5 5. A) log Simplify the expression B) log Find the exact value of log41 log4 without using a calculator. B) 1 4. Find the exact value of 1.50 ln e ln e without using a calculator. C) 1 Version 1 Page

6 4. Find the exact value of log 4 16 without using a calculator. D) 44. Expand the expression as a sum, difference, and/or constant multiple of logarithms. D) Condense the expression [log 4 x log 4 ] [log 4 y ] to the logarithm of a single term. 5 D) 5 x log4 y Determine whether or not x is a solution to 7 B) no 4x Determine whether or not ( x e 1) is a solution to ln(x 1). A) yes 54. Solve ln x 11 for x. D) 11/ 11/ e, e 57. Solve for x: x (6 x e e ) 9. Round to decimal places. C) Version 1 Page

7 59. Approximate the solution of 4x 1e 9 to decimal places. (You may use a graphing utility.) E) 0.1 Ans: E 6. Approximate the solution to ln( x) ln x 4. Round to decimal places. C) Use a graphing utility to approximate the solution to log6x log 6(x1). Round to decimal places. D) Glove and mitten warmers have become popular over the past few years. These devices consist of a paper pouch filled with a chemical mixture that reacts and releases heat when exposed to air. At a time t (in minutes) after being exposed to air at a temperature of o F, the temperature T of the pouch (in o F) can be modeled by the equation 1/ t T( t) 85e, 0 t 00 Find the time necessary for the warmer to reach a temperature of 106 o F. Round to the nearest tenth of a minute. E) 9.7 minutes Ans: E 68. An initial investment of $000 grows at an annual interest rate of 7% compounded continuously. How long will it take to double the investment? A) 9.90 years 70. The value of an investment is presently $ It had been paying 9% compounded continuously since the investment was made 10 years ago. How much was invested originally? B) $ How long will it take an investment that pays 4% compounded annually to double in value? Round to the nearest tenth of a year. A) 17.7 years Version 1 Page 4

8 74. What is the half-life of a radioactive substance if.4 g decays to 0.80 g in 40 hours? Round to the nearest tenth of an hour. A) 5. hours 75. The half-life of 14 Ba is 8.7 hours. How much of a 17. g sample of 14 Ba will be left after hours? Round to the nearest hundredth of a gram. C) 4.04 g 76. The population P of a culture of bacteria is described by the equation t P 1600e, where t is the time, in hours, relative to the time at which the population was What was the population at t = 5 hours? After how many hours will the population reach 11,000? Round to the nearest tenth of an hour. C) approximate population 18 when t 5 after.8 hours, P 11, The population P of a bacteria culture is modeled by 4100 kt P e, where t is the time in hours. If the population of the culture was 5800 after 40 hours, how long does it take for the population to double? Round to the nearest tenth of an hour. D) 79.9 hours 8. The decibel (db) is defined as db 10log P, where P is the power of a particular signal and P 1 is P 1 the power of some reference signal. In the case of sounds, the reference signal is a sound level that is just barely audible. How many dbs does a sound have if its power is 665,000 times that of the reference sound? Round to the nearest tenth. B) 58. db 8. It is against the law in some municipalities to play a car stereo so loud that the level of the sound is 75 db 50 feet from the source. The unit "db" refers to decibels and is defined as db 10log P, P 1 where P is the power density of the sound in question, and P 1 is a reference sound which is just barely audible, 10-1 watt/m. What is the level of sound as measured in dbs if 4 P 10 watts/m C) 84.8 db? Round to the nearest tenth. Version 1 Page 5

9 84. The chemical acidity of a solution is measured in units of ph: ph log[h ], where [H + ] is the hydrogen ion concentration in the solution. What is the ph if [H ] 7 10? Round to the nearest hundredth. D) The chemical acidity of a solution is measured in units of ph: ph log[h ], where [H + ] is the hydrogen ion concentration in the solution. If a sample of rain has a ph of., how many times higher is its [H + ] than pure water's, which has a ph of 7? D) Version 1 Page 6

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