Exponents and Logarithms Exam

Transcription

1 Name: Class: Date: Exponents and Logarithms Exam Multiple Choice Identify the choice that best completes the statement or answers the question.. The decay of a mass of a radioactive sample can be represented by an exponential equation in the form of t P y = ab. The initial mass of mg decreases in quantity through radioactive decay to 8 mg over a hour period. The half-life of the radioactive sample, in minutes, is approximately. a. 60 c. 40 b. 60 d. 60. Solve the following exponential equation: b 9x = b a. 0 c. b. d. x. The expression log x a. 8 log x 4log x is equivalent to c. log x b. 8 log x d. log x 4. The y-intercept of f( x) = a x b is a. a b c. a b b. b d. a b 5. The graph of f( x) = ab x, where 0 < b < and a < 0 undergoes the following transformation: y + = f( x 5). The range of the transformed graph is a. y < c. y > b. y > d. y <

2 Name: Use the following information to answer the next question A student s work to simplify an exponential equation is shown below: Step : log x + = log5 x Step : ( x + ) log = ( x) log5 Step : Step 4: Step 5: x log9 + log = log5 x log5 x log9 + x log5 = log5 log x = log5 log log4 6. The student made their first error when going from: a. Step to Step c. Step to Step 4 b. Step to Step d. Step 4 to Step 5 7. What is one half of 8 00? a c. 599 b d For the graph of y = log c ( x + ), where 0 < c <, the domain of this function is a. x > 4 c. x > b. x > d. x > 4 9. Written as a single logarithmic expression, logx logz + logy is x a. log c. log xy y z z b. log x z + y d. log x y z

3 Name: 0. Suppose that the future population of a small city can be determined by using the equation P = (.0) t where P is the future population and t is the fine in years from the present. An equation representing t and a function of P is logp a. t = logp 5 log.0 c. t = 5log.0 b. t = logp 5 log.0 d. t = P Which of the following statements are true based on the definition of a logarithmic equation: y = log a x I: x > 0 III: x II: a > 0 IV: a a. I, II and III only c. I, II and IV only b. I and IV only d. I, II only Use the following information to answer the next question Earthquake intensity is given by I = I 0 0 M, where I 0 is the reference intensity and M is the magnitude. Suppose that an earthquake measuring 6. on the Richter scale as recorded in Los Angeles is 70 times less intense as the reading recorded from a station in San Franscisco.. Determine, to the nearest tenth, the intensity of the earthquake recorded in San Francisco. a. 8. c. 7.8 b. 4.4 d..9. If log 8 = p and log q 56 = 8, determine the value of p log q 0. Round your answer to the nearest tenth. a. 9. c.. b. 0.8 d. 0.0 m 4. If log 5 m = Y, which expression below is equivalent to log 5 65 a. Y 4 c. Y 4 b. Y 4 d. Y 4

4 Name: 5. When the equation log a n = is solved for n in terms of a, where a > 0,a, the resulting equation is a. n = a c. n = a 9 b. n = a d. n = a 6 Short Answer 6. Numerical Response: Suppose that Kayla received a cheque from a distant relative for $5000 on her first birthday. If her parents invested this money into a trust and the value of this investment increased to $0 000 by her 8th birthday, what was her average annual rate of return on her trust? Round your answer to the nearest tenth of a percent. 7. Numerical Response: Suppose that $000 is invested in a savings account that earns 4.8% interest per annum, compounded monthly. What is the minimum number of years this investment need to remain in the account for its value to increase to at least $8000? Round your final answer to the nearest year. 8. Numerical Response: If the value of ( ab) = 4, then to the nearest hundredth, the value of log 5 a + log 5 b, where a,b > 0 is approximately. 9. Numerical Response: Suppose that a quantity of a particular type of steriod breaks down in the bloodstream at a rate of 5% every four hours. How long will it take for half of that quantity to remain in the blood stream. Round to the nearest hour. This process can be modelled by a exponential function of the form t p y = ab. 4

5 Name: 0. Numerical Response: Given that the equation, log c ( c) + log c ( c) = n, where n is a numerical value, what is the value of n? 5

6 Exponents and Logarithms Exam Answer Section MULTIPLE CHOICE. A. C. C 4. A 5. D 6. D 7. D 8. A 9. D 0. B. C. A. C 4. A 5. D SHORT ANSWER % per annum 7. 9 years hours 0..5 * + =.5*