Math 101 - Chapter - More Practice Name MUST SHOW WORK IN ALL PROBLEMS - Also, review all handouts from the chapter, and homework from the book. Write the equation in eponential form. 1) log 2 1 4 = -2 Write the equation in logarithmic form. 2) 73 = 343 3) Sketch the graph of the given function and its inverse in the same coordinate plane = (2) f-1() =... - - Solve for. If necessar, round the answer to two decimal places. 4) + 8 = 3 ) 10 = 4(2) - 120 6) log (0) = Solve the equation. 7) e( + 6) = 8 8) 7 2 b 2 + 4 9 = 8 9 9) 4 + ln() = 2 10) ln() = 2 11) ln(4-1) = 10 12) 7 b 3 + 9 = 7 2 Solve for. 13) log (64) = 2 1
14) log (2-10) = 3 1) log 3 () = 2 For the function, find a formula for the inverse function. 16) g() = log () 17) f() = 2 Find the logarithm. 18) log 4 (64) 19) log 4 ( 1 64 ) 20) log 27 (3) 21) log 4 ( 4) Solve the problem. 22) Some values of functions f, g, h, and k are provided in the table below.some of them are linear functions, and some are eponential. Find a possible equation for each function. f() g() h() k() 0 180 180 1/3 1 90 90 3 1 2 4 0 27 2 3 22. -90 243 3 4 11.2-180 2187 4 23) Complete the table below b using the table of values for f to complete the table of values for f-1. f() 1 121 2 111 3 101 4 91 f-1() 24) Let f() = 6. i) Find f(-2). ii) Find f-1(36). 2
2) Let f() = 4. a) Write the inverse function. b) Answer each of the following. Please show the "plug in" process, then evaluate. i) Find f(2). ii) Find f-1(1/4). iii) Find when f() = 1. iv) Find when f-1() = 3. Use a calculator to find the natural logarithm. 26) ln(0.982) Find the inverse of the given function. 27) f() = 7-8 Find the natural logarithm. 28) (eln6) 29) ln(e12) 30) (eln9) 31) ln(e7) Sketch the graph of the given function, its inverse, and = on the same set of aes. Graph the function with a solid line, and graph = and the function's inverse using dotted lines. 32) f() = 1 2-4 10-10 - 10 - -10 Find an equation of the eponential curve that passes through the given pair of points. 33) (0, ) and (3, 83) 3
Solve the problem. 34) The long jump record, in feet, at a particular school can be modeled b = 19.6 + 2.1 ln ( + 1) where is the number of ears since records began to be kept at the school. a) What is the record for the long jump 1 ears after record started being kept? Round our answer to the nearest tenth. b) When was the record 23.4 feet? 3) A communit is growing eponentiall according th the model f(t) = 4000(2.7)0.00t where t is the number of ears since 199, and f(t) is the number of people in the communit. a) How man residents are living in that cit in 2000. b) In what ear will the population be 4200 people? 36) The ph of a solution ranges from 0 to 14. An acid has a ph less than 7. Pure water is neutral and has a ph of 7. The ph of a solution is given b ph = - log(h+) where H+ represents the concentration of the hdrogen ions in the solution in moles per liter. Find the ph if the hdrogen ion concentration is 1 10-6. 37) Strontium 90 decas at a constant rate of 2.44% per ear. Therefore, the equation for the amount P of strontium 90 after t ears is P = P0 e-0.0244ṭ Write the equation in the case the initial amount of strontium is 1 grams. a) What will be the amount 1 ears later? b) How long will it take for 1 grams of strontium to deca to grams? Round answer to 2 decimal places. 38) The Richter scale converts seismographic readings into numbers for measuring the magnitude of an earthquake according to this function M() = log ( 10-3 ) where M is the magnitude, and is the seismographic reading. a) What would be the reading (to the nearest tenth) for a magnitud of 4.9? b) If the seismographic reading is 104, what is the magnitude of the earthquake? 39) Aleander received a gift from his grandfather of $4000, which he invested at an annuall compounded interest rate of 4%. Let V = f(t) represent the value (in dollars)of the account after t ears or an fraction thereafter. Find an equation for f. How much mone was invested after 17 ears? 40) The half-life of a radioactive element is 1 ears. There are 120 grams of this element present now. Let f(t) represent the number of grams that will be present t ears from now. i) Find an equation for f. ii) Use f to estimate the number of grams that will be present 20 ears from now. 41) A rumor is spreading across the CSM campus that there will be no finals for an classes this semester. At 8 a.m. toda, people have heard the rumor. Assume that after each hour, 4 times as man students have heard the rumor. Let f(t) represent the number of people who have heard the rumor t hours after 8 a.m. i) Find an equation for f. ii) Use f to predict the number of students who have heard the rumor b 1 p.m. iii) B what time we epect 320 to have heard the rumor. Please show all work. 4
Answer Ke Testname: CHAPTER-REV 1) 2-2 = 1 4 2) log 7 (343) = 3 3) - - 4) = -7.32 ) = 6.0768197 6) = 2.19 7) -3.92 8) ±0.36 9) = e-2/ 10) = e2 11) = 2.09726402 12) 1.6 13) = 8 14) = 67. 1) = 9 16) g-1() = 17) f-1() = log 2 () 18) 3 19) -3 20) 1 3 21) 1 2 22) f() = 180( 1 2 ) ; g() = -90 + 180; h() = (1/3)*9; k() = + 10 23) f() 1 121 2 111 3 101 4 91 f-1() 121 1 111 2 101 3 91 4
Answer Ke Testname: CHAPTER-REV 24) i) 1/36 ii) 2 2) i) 16 ii) -1 iii) 0 iv) 64 26) -0.0182 27) f-1() = 8 + 7 28) 6 29) 12 30) 9 31) 7 32) f-1() = 2 + 8 10-10 - 10 - -10 33) = (2.09) 34) a) 2.4 feet; b) ears after the records began to be kept. 3) a) 4100 people; b) 200 36) 6 37) a) 10.4 grms; b) 4.03 ears. 38) a) 79.4; b) 7 39) V = 4000(1.04)t; $7791.60 40) i) f(t) = 120( 1 2 )t/1 or f(t) = 120(0.948416)t ii) 47.6 grams 41) i) f(t) = (4)t ii) 120 students iii) 11 am 6