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2 Part 2. Free-response Questions- Show all your work for each of the problems. (1) Find the exact value for each logarithmic expression using the properties of logarithmic functions. (a) log3 (/27) (b) log, 56 – log27 (c) logs 4 (d) log, 4 + log, 9 (e) In (e®) (f) e(In 2) (0) B: 141.

2 Part 2. Free-response Questions- Show all your work for each of the problems. (1) Find the exact value for each logarithmic expression using the properties of logarithmic functions. (a) log3 (/27) (b) log, 56 – log27 (c) logs 4 (d) log, 4 + log, 9 (e) In (e®) (f) e(In 2) (0) B: 141.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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6:54 PM Wed Mar 30 62% Test 3 ... Calendar/Goals Test 4 Test 3 X MTH100 Extra Credit A... 2 Part 2. Free-response Questions- Show all your work for each of the problems. (1) Find the exact value for each logarithmic expression using the properties of logarithmic functions. (a) log3 (v27) (b) log2 56 – log2 7 (c) logg 4 (d) log6 4 + log, 9 (e) In (e®) (f) e(ln 2) (2) Find the exact solutions to each of the equations. (a) 0.0012- = 100*-2 (b) (4)3¤ = 64 (c) 2 log x = log 2 + log (3x – 4) (d) e2 + Зе* —4 %— 0. (3) Find the solution to each of the equations and correct the answer to two decimal places. (а) In (2.r — 3) %3D14 (b) 23"-1 = 5 (c) log x + log (x + 1) = log 12 (d) 21-1 = 32z+5 (4) Let f(x) = (})", g(x) = logį x, and h(æ) = 1 – log (x+ 3). (a) Graph the function f(x) = (G)" by plotting points (b) Graph g(x) = log i x using transformations of the graph of y = f(x) on the same xy-plane (c) State the transformations of the graph the basic log-function y = g(x) to obtain the graph of h(x) = 1 – log: (x + 3) and sketch the graph of y = h(x) using such transformations (d) State the domain, range and asymptote of each of the functions. (5) $12000 is invested at an interest rate of 10% per year. (a) Find the amount of the investment at the end of 10 years for each compounded method. (i) Semiannual (ii Monthly (iii) Continuously (b) After what period-of-time will the investment be doubled in value if compounded continuously? (6) A culture starts 8600 bacteria. After one hour the count is 10, 000. (a) Find a function that models the number of bacteria n(t) after t hours. (b) Find the number of bacteria after 2 hours. (c) After how many hours will the number of bacteria double? (7) The half-time of Palladium-100 is 4 days. After 20 days, a sample has been reduced to a mass of 0.375 g. (a) What is the initial mass of the sample? (b) Find a function that models the mass remaining after t days. (c) What is the mass after 3 days? (d) After how many days will only 0.15 g remain?
Transcribed Image Text:6:54 PM Wed Mar 30 62% Test 3 ... Calendar/Goals Test 4 Test 3 X MTH100 Extra Credit A... 2 Part 2. Free-response Questions- Show all your work for each of the problems. (1) Find the exact value for each logarithmic expression using the properties of logarithmic functions. (a) log3 (v27) (b) log2 56 – log2 7 (c) logg 4 (d) log6 4 + log, 9 (e) In (e®) (f) e(ln 2) (2) Find the exact solutions to each of the equations. (a) 0.0012- = 100*-2 (b) (4)3¤ = 64 (c) 2 log x = log 2 + log (3x – 4) (d) e2 + Зе* —4 %— 0. (3) Find the solution to each of the equations and correct the answer to two decimal places. (а) In (2.r — 3) %3D14 (b) 23"-1 = 5 (c) log x + log (x + 1) = log 12 (d) 21-1 = 32z+5 (4) Let f(x) = (})", g(x) = logį x, and h(æ) = 1 – log (x+ 3). (a) Graph the function f(x) = (G)" by plotting points (b) Graph g(x) = log i x using transformations of the graph of y = f(x) on the same xy-plane (c) State the transformations of the graph the basic log-function y = g(x) to obtain the graph of h(x) = 1 – log: (x + 3) and sketch the graph of y = h(x) using such transformations (d) State the domain, range and asymptote of each of the functions. (5) $12000 is invested at an interest rate of 10% per year. (a) Find the amount of the investment at the end of 10 years for each compounded method. (i) Semiannual (ii Monthly (iii) Continuously (b) After what period-of-time will the investment be doubled in value if compounded continuously? (6) A culture starts 8600 bacteria. After one hour the count is 10, 000. (a) Find a function that models the number of bacteria n(t) after t hours. (b) Find the number of bacteria after 2 hours. (c) After how many hours will the number of bacteria double? (7) The half-time of Palladium-100 is 4 days. After 20 days, a sample has been reduced to a mass of 0.375 g. (a) What is the initial mass of the sample? (b) Find a function that models the mass remaining after t days. (c) What is the mass after 3 days? (d) After how many days will only 0.15 g remain?
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