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CanSTEM Education Private School Inc. Part A: Short Answer Questions:Use separate sheets for answers. Attach them with question st J. Evaluate: log, 2 + log. 4 + log, 32 [K-1] 2 Explain and State the domain and range off (x) - , log [-4(x-12)] + 4 [C-2] R 1. Calculate log [T-2] 4. Which of the following statements will not be true regarding the graphs off(x) - log, (3x), g(x) - log, (9x). h(x) = log, (#)? [T-2] a) They will all have the same vertical asymptote b) They will all have the same x-intercept c) They will all curve in the same direction d) They will all have the same domain $. The half-life of a certain element is 20 minutes. You weigh the element and record 80 grams. What is the instantaneous rate of change per minute 1.5 hours after your initial weighing? [A-1] 6.Suppose the population of a given towm is increasing for a given period of time. What can you tell about its instantaneous rate of change of the population during that period? [A-1] a) The instantaneous rate of change continues to get larger during the entire interval. b) The instantaneous rate of change will be positive at cach point in the interval. c) The instantaneous rate of change may be zero, but can not be negative. d) The instantaneous rate of change at any point in the interval will be larger than the average rate of change for the interval. Part B: Full Solution Questions 7. Solve for x: 64'-1 = 81/8 [K-2] 8. Solve for x: 10"*2 - 10" = 9900 [K=3] 9. Solve for x; log (x + 3) + log x = 1. [K=4] 10. Two friends are walking, having a normal conversation with loudness of 60 db. When they get near a busy street, they have to double the intensity of the sound to be able to hear each other. Calculate the new sound level if the formula is Z - - 10 log( 70-17) [A=3] CanSTEM Education Private School Inc. The relationship between pit and Hydrogenion concentration is given by the formula PH =-logCH , where ph is the measure of acidity or alkalinity of a substance and HT is concentration of hydrogen tons ( ) 11. Compare the strength of acids at the different points of the PH scale using the formula pH = - log[H ] a) Does adding two to a pH at one end of the scale (going from a pH from 1 to 3) have the same effect as adding two to a pH at the other end of the scale (going from a pH of 10 to 12)? Support your conclusions by comparing the strength of the acid. [A=3] b) Does doubling the pH from 2 to 4 have the same effect as doubling pH from 5 to 10? Support your conclusions. [A=3] 12. A box of tissues cost $2.50 at the end of 2010. Assume prices go up 5% very year. What year will it be when the tissues cost $5.00? [A=4] 13. State the transformations, in proper order, that are needed to turn ((x) = -3log, x + 1 into g(x) = 5log2 x - 2, then sketch f(x), labeling significant points . Graph on the separate paper. [C=4] 14. Which of the following characteristics of the function f(x) = log x changes under the following transformation(x) -g(x) = 1 - 2log (6x)? Explain. [C=4] a) The range b) The domain c) The x-intercept d) The vertical asymptote 15. Solve: 25" -4 (5) = 12 [T=3] 16. Derive the quotient law of logarithms from the quotient law of exponents without using the product [T-4] law 17. Solve for x accurate to 2 decimal places: log,(x - 1) - log,(x + 2) + log,(x + 3) =2 [T=4]
