Chapter 4-5 Cumulative Test Review

Chapter 4-5 Cumulative Test Review Name____________________________________________Period:____________ Write the expression as a single logarithm with coefficient 1. Assume all variables represent positive real numbers with a 1 and b 1. 1 1 1 11) log2 x4 + log2 x 4 - log2 x 2 4 6 log2 ( x17/6 ) Use the definition of inverses to determine whether f and g are inverses. 1 1) f(x) = 6x - 6, g(x) = x + 1 6 Yes 2) f(x) = 4 5x + 4 , g(x) = x+5 x No Solve the problem. 12) The logarithmic function f(x) = -100 + 87 ln x models the number of visitors (in millions) to a certain country's museums, where x is the number of years since the initial recording of the number of visitors. Use this function to estimate the number of visitors in year 50. Round to the nearest tenth of a year. 240.3 million Find the function value. If the result is irrational, round your answer to the nearest thousandth. 3) Let f(x) = 6 x. Find f(2). 36 Find the future value. 4) $5337.27 invested for 9 years at 4% compounded monthly Solve the equation. Round to the nearest thousandth. 13) 3 x = 11 {2.183} $7645.49 Solve the problem. 5) The decay of 119 mg of an isotope is given by A(t)= 119e-0.018t, where t is time in years since Solve the equation and express the solution in exact form. 14) ln(5x - 6) + ln (x - 6) = ln 36 36 the initial amount of 119 mg was present. Find the amount (to the nearest milligram) left after 36 years. 62 5 15) ln ex - ln e6 = ln e4 {10} Solve the problem. 16) What is the rate on an investment that doubles $8296 in 17 years? Assume interest is compounded quarterly. 4.1% Evaluate the logarithm. 6) log 6 6 1 Write in logarithmic form. 7) 5 3 = 125 log 125 = 3 5 Solve the following graphically. If necessary, round answers to the nearest thousandth. 3 17) ln (x - 3) = - x + 0 {3.228} Write an equivalent expression in exponential form. 8) log 1024 = 5 4 4 5 = 1024 Solve the equation. 9) log1/3(x + 7) = -2 18) ex + ln 10 = 7ex 2 Solve the problem. 19) Suppose the number of Quickie hamburgers (in millions) served yearly can be modeled by f(x) = 35.8e0.17x. Approximate how many Use the properties of logarithms to rewrite the expression. Simplify the result if possible. Assume all variables represent positive real numbers. x 3 y8 10) log2 9 years it takes for the number of hamburgers served to reach 67 million. Round to the nearest year. 4 yr 3 log2 x + 8 log2 y - log2 9 1 Solve the system using matrices. 20) x + y = 0 {(7, -7)} x - y = 14 21) 4x + 9y = 81 -2x - 7y = -63 -3 4 31) -2 -1 -6 9 3x + 9y 6k - 7z 32) -8w + 9v 4m - 2n {(0, 9)} 22) 3x - y - 6z = -17 -7x + 8y + 4z = 11 7x - 6y + z = 13 {(3, 2, 4)} 9x + 16y 14k - 3z -6w + 7v 2m + 4n -6x - 7y - -8k - 4z -2w + 2v 2m - 6n 34) Let A = 2 3 24 and B = {(-1, 2, -2, 1)} 2 3 9 3 -1 9 -8 -8 -1 36) [ -3 -3 -1] Solve the problem. 37) Given A = 4 4 5 62 3 5 9 90 2 -2 7 34 [2 -2 -8 6] 0 4 . Find 2A + B. -1 6 Find the matrix product when possible. 35) 0 -1 -2 0 4 1 -1 1 Write the augmented matrix for the system. Do not solve the system. 6 6 -6 25) 6x + 6y = -6 9 7 -11 9x + 7y = -11 26) 4x + 4y + 5z = 62 3x + 5y + 9z = 90 2x - 2y + 7z = 34 -9 0 4 3 -9 13 -6 -4 6 4 -3 4 Find the indicated matrix. 33) Let B = [-1 1 4 -3]. Find -2B. 23) 4x + y + z = -4 x - y + 2z = 2 4x + y + z = 2 24) -2x + y + 3z - w = -3 -x - 2y + z - 3w = -8 -2x + 3y - 2z + w = 13 3x - y - z - 3w = -6 + 5 -3 , find A3 . -2 4 1 -1 -9 1 [-7 2 -53] 209 -201 -134 142 Decide whether or not the matrices are inverses of each other. 1 1 2 2 38) -5 1 and 7 Yes 5 -7 1 2 2 Solve the problem using matrices. 27) Jerry has three pieces of string. The total length is 107 cm. The sum of the two longer pieces is 88 cm. The middle piece is twice as long as the shortest piece. What are the lengths of the three pieces? 19 cm; 38 cm; 50 cm 2 -1 0 39) -1 1 -2 Solve the problem. 28) Find the dimensions of a rectangular enclosure with perimeter 34 ft and area 60 ft2 . 1 0 -1 12 ft by 5 ft 1 -1 2 and -3 -2 4 -1 1 1 No Solve the problem. 40) A company makes 3 types of cable. Cable A requires 3 black, 3 white, and 2 red wires. B requires 1 black, 2 white, and 1 red. C requires 2 black, 1 white, and 2 red. The company used 100 black, 110 white and 85 red wires. How many of each type of cable were made? Find the values of the variables for which the statement is true, if possible. x = 2; y = 4; k = -9 29) x + 3 y + 4 = 5 8 7 7 k -9 Perform the operation or operations when possible. 30) -1 0 - -1 3 0 -3 31 31 0 0 15 A; 25 B; 15 C 2 4 10 3 14