MATH lll FZol) Practice Test 3bSHOWALL WORKNO CREDIT WILL BE GIVEN FOR THE ANSWERS WITHOUT WORK4 points eachl. Write each equation in its equivalent exponential forma)2= log5x b) 3 : log b c)ln7 =y2. Write each equation in its equivalent logarithmic forma) 122:y b) b3 = 8 c) eY: l03. Expand each logarithmic expressiona) rog(r'f),,,(,F)4. Combine each logarithmic expressiona) 0.5 log x + 4 log(x - 1) b) 4 ln x-21n6 + 0.5 ln y5. The function y = 2.557(1.017)* describes the world population, in billions, x yearsafter 1949. Rewrite the model in terms of the base e.6. The growttr model a: 1049 e 0'017t describes Mexico's population t years after 2003.a) What is Mexico's growth rate rnYo?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 ofI.5Yo per year. Find the exponential model to describe the population of Japan x yearsafter 2005.8. Solve for x:a)3t-* :l/21 b)30-(1.4;*:9 c)6+2lnx:5 d)loga(3x+2):39. The formula A = 18.9 e 0'0055t models the population of New-York State, in millions, tyears after 2000. When will the population of New-York reach 19.54 million?10. Find (g(x)) and g(f(x)) for (x):5x - 9 and g(x): (x + 5)/911. Find the inverse ftlx; ina) f(x) : 2x +! b) (x) = ln (3/x)x-312.Theregular price of a computer is x dollars. Let (x) : x - 400 and g(x) : 0.75xa) 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 thecomputer. Which of them models the greater discount on the computer?13. Use hansformations to sketch the graphsa) y: - log(x +2)b)y=2lx-31+114. Find the direction the parabola opens, x- and y-coordinates of the vertex, y-intercept,and graph the function:a)yl -2(x-3;2+ 8 b)y: * -zx+tANSWERS1.a)52:x b)103:b c)eY:72. a)2: logrzx b)3 : lo968 c) y: lnl03. a)2logx +0.5log y b) (1/3)ln x - ln 36 - 4 ln y4. a) toe6l;(.r -1)o) rlr"({P)5. Y: 2.557e0'or7*6. a) 1.7% b) 4l years'l.P=127.2e0'or5t8. a) 4 b) 10.1I c) 0.61 d) 62139.200610. f(g(x)) : (5x - 56)19, g((x) : (5x - 4y9ll. a) (3x+l/(x-2) b) 3/e.12. a) f represents the price after $400 discount and g represents the price after 25o/odiscount.b) (g(x)) :0.75x- 400, represents an additional $400 discount on a price that havealready been reduced by 25%; g(f(x)) : 0.75x - 300, represents an additional25o/odiscount on a price that has already been reduced by $400. f(g(x)) gives a lower priceafter 2 discounts.13. a) .^14. a) opens downward, vertex (3,8), y-intercept (0, -10); b) opens upward, vertex (1,0),y-intercept