Math Reviewing Chapter 4

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1 Math 80 - Reviewing Chapter Name If the following defines a one-to-one function, find the inverse. ) {(-, 8), (, 8), (-, -)} Decide whether or not the functions are inverses of each other. ) f() = + 7; g() = - 7 Determine the inverse of the given function. ) {(-, ), (-, ), (0, ), (, ), (, 7)} The graph of a one-to-one function f is given. Draw the graph of the inverse function f- as a dashed line or curve. ) f() = Use the graph of the given one-to-one function to sketch the graph of the inverse function. For convenience, the graph of = is also given. ) (, ) (-, ) (0, ) (-, -) The function f is one-to-one. Find its inverse. 6) f() = + 7) Determine the equation for the inverse function of = ( + ) - 8.

2 Solve the problem. 8) The profit P for selling items is given b the equation P() = Epress the sales amount as a function of the profit P. Approimate each value using a calculator. Epress answer rounded to three decimal places. 9). p Solve the problem. 0) A rumor that there will be an open book test on chapter has spread in our class of 8 students. The mathematical model for the situation is N = 00( - e-0.6d) where N is the number of students who have heard the rumor and d is the number of hours that have elapsed since the rumor began. a) How man students will have heard the rumor after hours? b) students have heard the rumor. How man hours ago did the rumor began? c) DON'T EVEN DREAM ABOUT IT. Graph the function. ) Graph the function f() = - - Answer the question. ) Define the number e. A) The number approimatel equal to.7. lim B) The number defined b e = n «+ n in Calculus. n C) The number that the epression, + n n, approaches as n «. Solve the equation. D) All of the above. ) 9 œ 7( - ) = 9 ) ( - )= 6 Change eponential epressions to logarithmic epression ). + = Convert to logarithmic form. 6) e = Convert to eponential form. 7) log = - Change logarithmic epression to eponential epression. 8) logb 9 = Find the value of the epression. 9) log 9 8

3 0) ln l Solve the problem. ) The number of men ding of AIDS (in thousands) since 987 is modeled b = (ln ), where represents the number of ears after 987. Use this model to predict the number of AIDS deaths among men in 99. Epress answer rounded to the nearest hundred men. Find the domain of the function. ) f() = log 0 ( ) ) Determine the domain of the function f() = log / ( + ). The graph of a logarithmic function is shown. Select the function which matches the graph. ) Solve the problem. ) log 8 7 = 6) log 6 = 7) The Richter scale converts seismographic readings into numbers for measuring the magnitude of an earthquake according to this function M() = log ( o ), where o = 0-. What would be the readings (to the nearest tenth) for magnitudes of.9 and 7.9? 8) The formula D = 6e-0.0h can be used to find the number of milligrams D of a certain drug in a patient's bloodstream h hours after the drug has been given. When the number of milligrams reaches, the drug is to be given again. What is the time between injections? 9) ph = -log 0 [H+] Find the [H+] if the ph =.. 0) ph = -log 0 [H+] Find the ph if the [H+] =.7 0-.

4 Use the properties of logarithms to find the eact value of the epression. Do not use a calculator. ) log 7 70 ) log - log 6 Using the properties of logarithms, evaluate the epression. ) ln e. Write as the sum and/or difference of logs. Do not use eponents. ) log 9 8 r s Epress as a single logarithm. ) ( log a m - log a n) + log a k Write epressions as a single logarithm. 6) ln 6 - ln( - - ) Use the Change-of-Base Formula and a calculator to evaluate the logarithm. Round our answer to two decimal places. 7) Evaluate log (/) 9. Graph the function using a graphing utilit and the Change-of-Base Formula. 8) = log( - ) Solve the equation. 9) log = log + log ( - ) 0) log ( + ) - log ( - ) = log Solve the given logarithmic equation. ) log( - ) - log( - ) = ) + log( + ) - log =

5 Solve the given eponential equation. ) œ t - = 7 Solve the equation. If necessar, round our answer to two decimal places. ) ( ) = Use a graphing calculator to solve the equation. Round our answer to two decimal places. ) log + log = Solve the problem. 6) The size P of a small herbivore population at time t (in ears) obes the function P(t) = 00e0.7t if the have enough food and the predator population stas constant. After how man ears will the population reach 00? 7) A culture of bacteria obes the law of uninhibited growth. If 0,000 bacteria are present initiall and there are 609,000 after 6 hours, how long will it take for the population to reach one million? 8) The half-life of silicon- is 70 ears. If 0 grams is present now, how much will be present in 00 ears? (Round our answer to three decimal places.) 9) A fossilized leaf contains % of its normal amount of carbon. How old is the fossil (to the nearest ear)? Use 600 ears as the half-life of carbon. 0) Strontium 90 decas at a constant rate of.% per ear. Therefore, the equation for the amount P of strontium 90 after t ears is P = P0 e-0.0t. How long will it take for grams of strontium to deca to grams? Round answer to decimal places. ) The amount of a certain drug in the bloodstream is modeled b the function = 0 e- 0.0t, where 0 is the amount of the drug injected (in milligrams) and t is the elapsed time (in hours). Suppose that 0 milligrams are injected at 0:00 A.M. If a second injection is to be administered when there is milligram of the drug present in the bloodstream, approimatel when should the net dose be given? Epress our answer to the nearest quarter hour. ) A thermometer reading 79eF is placed inside a cold storage room with a constant temperature of ef. If the thermometer reads 7eF in minutes, how long before it reaches 7eF? Assume the cooling follows Newton's Law of Cooling: U = T + (Uo - T)ekt. (Round our answer to the nearest whole minute.) ) A cup of coffee is heated to 9eand is then allowed to cool in a room whose air temperature is 7e. After minutes, the temperature of the cup of coffee is 0e. Find the time needed for the coffee to cool to a temperature of 0e. ) The logistic growth model P(t) = 0 represents the population of a bacterium in a culture tube + 0.e-0.t after t hours. What was the initial amount of bacteria in the population?

6 80 ) The logistic growth model P(t) = represents the population of a species introduced into a new + e-0.88t territor after t ears. When will the population be 80? 6) A life insurance compan uses the following rate table for annual premiums for women for term life insurance. Use a graphing utilit to fit an eponential function to the data. Predict the annual premium for a woman aged 70 ears. Age Premium $0 $ $90 $ $60 $0 $88 7) After introducing an inhibitor into a culture of luminescent bacteria, a scientist monitors the luminosit produced b the culture. Use a graphing utilit to fit a logarithmic function to the data. Predict the luminosit after 0 hours. Time, hrs 8 0 Luminosit ) A mechanic is testing the cooling sstem of a boat engine. He measures the engine's temperature over time. Use a graphing utilit to fit a logistic function to the data. What is the carring capacit of the cooling sstem? time, min 0 0 temperature, ef

7 Answer Ke Testname: CHAPTER ) Not a one-to-one function ) No ) {(, -), (, -), (, 0), (, ), (7, )} ) ) (, ) (, 0) (, -) - (-, -) 6) f-() = ) = + 8-8) (P) = P + 0 9) ) students, 9 hours 7

8 Answer Ke Testname: CHAPTER ) ) D ) = - ) = or = - ) log. = + 6) ln = 7) - = 8) b/ = 9 9) - 0) 0 ) 6,900 ) (-«, 8) U (9, «) ) (-, «) ) = - log (-) ) { } 6) {} 7).7 and.9 8) 0. hrs 9) ). ) 0 ) ) 8. ) log log 9 r - log 9 s ) log a mk n 6) ln( 8 ) 7)

9 Answer Ke Testname: CHAPTER 8) ) {-} 0) {} ) = 6 ) = 7 ) t = ) {-.90} ).8 6) 6.6 rs 7) 8.0 hours 8).90 9),86 0).0 ears. ) : P.M ) 7 minutes ) 6. minutes ) 0 ) 8.9 ears 6) = 8.9e0.068, $0 7) = ln (), ) = e-0.6, ef 9

MAC 1105 Review for Exam 4. Name

MAC 1105 Review for Exam 4. Name MAC 1105 Review for Eam Name For the given functions f and g, find the requested composite function. 1) f() = +, g() = 8-7; Find (f g)(). 1) Find the domain of the composite function f g. 9 ) f() = + 9;