# Chapters 8 & 9 Review for Final

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1 Math Intermediate Algebra Professor Valdez Chapters 8 & 9 Review for Final SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Solve the formula for the indicated letter. 1) A = 1 3 πr2 for r > 0 1) Solve. 2) (9 + 3) 2-6 = 0 2) 3) = ) Solve the problem. 4) The weekl revenue R of a compan that sells to trucks is given b R = ( ). 4) How man units must be sold so the compan makes a weekl revenue of \$60,000? Use the discriminant to determine the number and tpe of solutions for the equation. ) = 0 ) Use the discriminant of the equation to determine the number of -intercepts. 6) f() = ) 7) f() = ) Graph the function function. 8) f() = ) Solve the problem. 9) The cost in millions of dollars for a compan to manufacture thousand automobiles is given b the function C() = Find the number of automobiles that must be produced to minimize the cost. 9) 1

2 10) A to rocket is launched straight upward with an initial velocit of 32 feet per second from a 4-foot high platform. The height h, in feet, of the rocket above ground t sec after it is launched is modeled b the function h(t) = -16t t ) i) When will the rocket reach its maimum height? What is that height? ii) How man seconds does it take until the rocket hits the ground? Round to the nearest tenth of a second if necessar. Solve the equation. 11) = 0 11) 12) (m + 4) 2/3 + 9(m + 4) 1/ = 0 12) Write a quadratic equation having the given numbers as solutions. 13) 9, onl solution 13) 14) - 4, 7 14) 1) 2i, -2i 1) Solve. Then graph the solution. 16) < 0 16) ) ) Graph the function function. 18) f() = (3) 18) Given f() and g(), perform the indicated operation. 19) f() = ; g() = -4-4 Find (f + g)(). 19) 2

3 20) f() = + 4 ; g() = - 4 Find (f g)(). Given f() and g(), find the composition. 21) f() = ; g() = 4-6 Find (g f)(). 20) 21) 22) f() = 3 ; g() = 2-1 Find (f g)(-13). 22) Evaluate. 23) Find (f/g)(4) given f() = and g() = ) Determine whether the function whose graph is shown is a one-to-one function. 24) 24) Given the graph of a one-to-one function, sketch the graph of its inverse. 2) 2) Find the inverse of the function represented b the set of ordered pairs. 26) f: {(-1, 14), (11, -14), (-20, 10)} 26) 3

4 Find the inverse of the following one-to-one function. 27) f() = ) 28) f() = ) Decide whether or not the functions are inverses of each other. 29) f() = 9 + 4, g() = ) 30) f() = 3 7-8, g() = ) Evaluate the function for the given value. 31) f() = 6 1- ; f(4) 31) Solve. 32) = ) Solve the problem. 33) The number of bacteria growing in an incubation culture increases with time according to B() = 900(3), where is time in das. What was the initial number of bacteria in the incubation culture? 34) The half-life of a certain radioactive substance is 14 ears. Suppose that at time t = 0, there are 27 g of the substance. Then after t ears, the number of grams of the substance remaining will be N(t) = 27 1 t/28. How man grams of the 2 33) 34) substance will remain after 70 ears? Round to the nearest tenth. 3) What will be the amount in an account with initial principal \$000 if interest is compounded continuousl at an annual rate of 3.2% for 6 ears? 3) Write the logarithmic equation in its equivalent eponential form. 36) log 7 49 = 2 36) 4

5 Write the eponential equation in its equivalent logarithmic form. 37) 1-2 = 2 37) Solve. Round the answer to three decimal places. 38) 4-3 = 21 38) Evaluate. 39) log ) 40) log 40) 41) log ) Write the epression as the sum or difference of logarithms. 42) log 4 (16 9) 42) 43) log m m + 16 m ) Evaluate. 44) log 19 44) 4) ln e 9 4) 46) 10 log 9 46) Solve. 47) The formula for the ph of a solution is given b the logarithmic equation ph = -log [H + ], where [H + ] is the concentration of hdrogen ions. The concentration of hdrogen ions of a specific solution is Calculate the ph of this solution. Provide an appropriate response. 48) Write the epression as a single logarithm: 47) 48) log b ( - 3) - 6 log b

6 Write the epression as the sum or difference of logarithms. 49) log b 4 9 b ) Solve. 0) log 4 = 3 0) 1) log 8 2 = 1) 2) log 2 ( + 4) + log 2 ( - 2) = 4 2) Use a calculator to approimate the logarithm to four decimal places. 3) log ) Solve the problem. 4) The size P of a rabbit population at time t (in ears) is modeled b the function P(t) = 600e 0.16t. 4) After how man ears will the population reach 3000? Round to the nearest hundredth. ) \$600 is invested at 4% compounded quarterl. In how man ears will the account have grown to \$8000? Round our answer to the nearest tenth of a ear. ) 6

7 Answer Ke Testname: CHAPTERS 8 AND 9 REVIEW 1) r = 3A π 2) , ) 2 + i 38 6, 2 - i ) 2340 units ) Two real-number solutions 6) One -intercept 7) No -intercepts 8) Verte: (1,4); ais of sm: = 1; -intercepts: (-1,0), (3,0); -intercept: (0,3) ) 4 thousand automobiles 10) i) 20 ft in 1 sec ii) 2.1 sec 11) ±1, ± 3 12) -129, ) = 0 14) = 0 1) = 0 16) (-3, ) ) - 7 4,

8 Answer Ke Testname: CHAPTERS 8 AND 9 REVIEW 18) ) , -4, ) ) (g f)() = ) -3 23) ) Not one-to-one 2) ) f -1 : {(14, -1), (-14, 11), (10, -20)} 27) f -1 () = ) f -1 () = ) Not inverses 30) Inverses 8

9 Answer Ke Testname: CHAPTERS 8 AND 9 REVIEW 31) ) -3 33) ) 4.8 g 3) \$ ) 7 2 = 49 37) log 1/ 2 = -2 38) ) -2 40) ) 0 42) 2 + log ) log m (m + 16 ) - log m (m + 13 ) 44) 19 4) 9 46) 9 47) 6 48) log b ( - 3) 6 49) 9 4 log b + 2-2log b 0) 64 1) 1 3 2) 4 3) ) r ).2 ears 9

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