MATH lll FZol Practice Test 3b SHOWALL WORK NO CREDIT WILL BE GIVEN FOR THE ANSWERS WITHOUT WORK 4 points each l Write each equation in its equivalent exponential form c ln7 y a 2 b 3 log log5x b 2 Write each equation in its equivalent logarithmic form c eY l0 a b b3 8 122 y 3 Expand each logarithmic expression a F rog r f 4 Combine each logarithmic expression b 4 ln a 0 5 log x 4 log x 1 x 21n6 0 5 ln y 5 The function y 2 557 1 017 describes the world population in billions x years after 1949 Rewrite the model in terms of the base e a 0 017t describes Mexico s population t years after 2003 1049 e 6 The growttr model growth rate rnYo a What is Mexico s b How long will it take Mexico to double its population 7 The population of Japan was 127 2 million in 2005 growing with a continuous rate of I 5Yo per year Find the exponential model to describe the population of Japan x years after 2005 8 Solve for x a 3t l 21 b 30 1 4 9 c 6 2lnx 5 0 0055t d loga 3x 2 3 models the population of New York State in millions 9 The formula A 18 9 e years after 2000 When will the population of New York reach 19 54 million 10 Find g x and g f x for 11 Find the inverse a f x 2x x 3 x 5x 9 and g x t x 5 9 ftlx in b x ln 3 x 12 Theregular price of a computer is x dollars Let x x 400 and g x 0 75x a Describe what the functions f x and g x model in terms of the price of the computer b Find g x and g f x describe what do they represent in terms of the price of the computer Which of them models the greater discount on the computer 13 Use hansformations to sketch the graphs b y 2lx 31 1 a log x 2 y 14 Find the direction the parabola opens and graph the function a yl 2 x 3 2 8 x and y coordinates of the vertex y intercept b y zx t ANSWERS 1 a 52 x b 103 b c eY 7 2 a 2 logrzx b 3 lo968 c y lnl0 3 a 2logx 0 5log y b 1 3 ln x ln 36 4 ln y 4 a toe6l r 1 o 5 Y 6 a rlr P 2 557e0 or7 1 7 b 4l years l P 127 2e0 or5t 8 a 4 b 10 1I c 0 61 d 6213 9 2006 10 f g x 5x 56 19 g x 5x ll a 12 a 3x l x 2 b 3 e 4y9 f represents the price after 400 discount and g represents the price after 25o o discount b g x 0 75x 400 represents an additional 400 discount on a price that have already been reduced by 25 g f x 0 75x 300 represents an additional25o o discount on a price that has already been reduced by 400 f g x gives a lower price after 2 discounts 13 a b y 14 a opens downward vertex 3 8 y intercept 0 10 b opens upward vertex 1 0 y intercept 0 1