Ch. Review College Algebra Name SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. Decide whether or not the functions are inverses of each other. 3 5 + 3 ) f() =, g() = + 5 ) If the following defines a one-to-one function, find its inverse. If not, write ʺNot one-to-one.ʺ ) {(-, ), (, -), (8, -), (-8, )} ) If f is one-to-one, find an equation for its inverse. 3) f() = 33-3) Find the domain and range of the inverse of the given function. ) f() = - 5 ) Find the function value. If the result is irrational, round our answer to the nearest thousandth. 5) Let f() = 3. Find f(-3). 5) Graph the function. ) f() = ) - - - - - - 7) f() = - 7) - - - - - -
Solve the equation. 8) - = 8 8) 9) (5-3) = 9) 0) 7 + = 3-0) ) e3 - = (e5) - ) ) e - = e + ) Find the future value. 3) $07 invested for 5 ears at 7% compounded quarterl 3) Find the present value of the future value. ) $000, invested for 9 ears at 0% compounded monthl ) Evaluate the logarithm. 5) log 5) ) log 5 5 ) 7) log 0 7) Write in logarithmic form. 8) -3 = 8 8) 9) 3/ = 8 9) Write an equivalent epression in eponential form. 0) log 5 = 0) Solve the equation. ) log 0 = ) ) log 8 = 3 ) 3) log 3 = - 3)
Graph the function. ) f() = log ) - - - - - - Write the epression as a sum, difference, or product of logarithms. Assume that all variables represent positive real numbers. 5) log 9 8 5) Use the product, quotient, and power rules of logarithms to rewrite the epression as a single logarithm. Assume that all variables represent positive real numbers. ) 3 log 3 + log 3-9 log 3 ) Given log 0 = 0.300 and log 0 3 = 0.77, find the logarithm without using a calculator. 7) log 0 7 7) Provide an appropriate response. 8) Use a propert of logarithms to evaluate log 9. 8) Use a calculator to find the logarithm. Give an approimation to four decimal places. 9) log.0800 9) 30) ln 300 30) Use the change of base rule to find the logarithm to four decimal places. 3) log 7 79.77 3) 3) log 9 9.0 3) 3
Solve the problem. 33) Let u = ln a and v = ln b. Write the following epression in terms of u and v without using the function ln. ln a 9 b8 33) 3) The loudness of a sound can be quantified in units called decibels, where the number of decibels d is given b the formula d = 0 log I Io. 3) What is the decibel rating of a sound having an intensit I = 0,000 I0? Provide an appropriate response. 35) Given f() = ln, evaluate the following. (a) f(e3) (b) f(eln 3) (c) f(e3 ln 3) 35) 3) With the function f() = log a, wh canʹt be less than 0? 3) 37) Wh canʹt be the base of a logarithmic function? 37) Solve the equation. If necessar, round to the nearest thousandth. 38) = 8 38) 39) e9 e = e5 39) Solve the equation and epress the solution in eact form. 0) ln(8 + 3) = ln 0) ) log ( - 3) = - log ) ) ln(-) + ln = ln(3-9) ) Solve the equation. 3) ln e - ln e7 = ln e8 3) ) log3(log3 ) = ) Solve for the indicated variable. 5) P = 30,000 et/5, for t 5) Solve the problem. ) The growth in population of a cit can be seen using the formula p(t) = 9759e0.00t, where t is the number of ears since 9. Use this formula to calculate the population in 9. )
7) What is the rate on an investment that triples $38 in 7 ears? Assume interest is compounded monthl. 7) 8) A sample of 50 grams of radioactive substance decas according to the function A(t) = 50e-.03t, where t is the time in ears. How much of the substance will be left in the sample after 30 ears? Round our answer to the nearest whole gram. 8) 9) A certain radioactive isotope has a half-life of approimatel 700 ears. How man ears to the nearest ear would be required for a given amount of this isotope to deca to 5% of that amount? 9) 50) The population growth of an animal species is described b F(t) = 00 log (t + 3) where t is measured in months. Find the population of this species in an area months after the species is introduced. 50) 5) The number of books in a small librar increases according to the function B = 9000e0.0t, where t is measured in ears. How man books will the librar have after ears? 5) 5) How long will it take for prices in the econom to double at a 0% annual inflation rate? 5) Solve. 53) In a town whose population is 500, a disease creates an epidemic. The number N of people infected t das after the disease has begun is given b the function 53) N(t) = 500 + 7 e-0.5t Find the number infected after 5 das. 5) A lake is stocked with 33 fish of a new variet. The size of the lake, the availabilit of food, and the number of other fish restrict growth in the lake to a limiting value of 95. The population of fish in the lake after time t, in months, is given b the function 5) P(t) = 95 +.75e-0.37t. After how man months will the population be 0? 5
Answer Ke Testname: M3CHR ) No ) {(, -), (-, ), (-, 8), (, -8)} 3) f-() = 3 + 3 ) Domain: [0, ); range: [5, ) 5) 7 ) - - - - 7) - - - - - - - 8) {3} 9) {3} - 0) - ) 8 ) - 7 5 3) $580.9 ) $3.35 5) - ) 7) 0 8) log 8 = -3
Answer Ke Testname: M3CHR 9) log 8 = 3 0) 5/ = ) {5} ) {} 3) ) - - - - - - 5) log + log 9 - log 8 ) log 3 ( /9) 7) 0.893 8) 9 9) -.099 30) 5.7038 3).50 3).355 33) 9 u - v 3) 0 decibels 35) (a) 3 (b) ln 3 (c) 3 ln 3 or ln 7 3) Answers ma var. One possibilit: The function is defined for all positive numbers a, a. Since a positive number raised to an real-number eponent is a positive number, must be positive, too. That begs the question of wh a must be positive. Assume that a is a negative number. A negative number raised to certain powers (e.g., /) would ield a non-real number. 37) Answers ma var. One possibilit: If the base of a logarithm were, as in = log, then for all values of, would equal. A function requires each -coordinate to have a unique -coordinate. Thus, the equation = log, whose graph would be equivalent to the line =, would not be a function. 38) {.085} 39) {0.333} 0) 9 ) 5 ) 3) {5} 7
Answer Ke Testname: M3CHR ) {7} P 5) t = 5 ln 30,000 ) 995 7) 5.8% 8) 90 grams 9) 300 ears 50) 70 5), 5) 7.7 ears 53) 0 5) 5 8