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Magazine Problem 52
Graph by hand or using a graphing calculator and state the domain and the range of each function. $$ f(x)=e^{x+3} $$
Problem 52
For each function, (a) determine whether it is one-to-one and (b) if it is one-to-one, find a formula for the inverse. $$f(x)=3 x$$
Problem 53
Graph by hand or using a graphing calculator and state the domain and the range of each function. $$ f(x)=-e^{x} $$
Problem 53
For each function, (a) determine whether it is one-to-one and (b) if it is one-to-one, find a formula for the inverse. $$g(x)=3 x-1$$
Problem 53
Express as an equivalent expression that is a single logarithm and, if possible, simplify. $$\log _{a}\left(x^{2}-4\right)-\log _{a}(x+2)$$
Problem 53
Solve. Where appropriate, include approximations to three decimal places. $$ \log (2 x+1)=\log 5 $$
Problem 53
Solve The percent of smokers \(P(t)\) who, with telephone counseling to quit smoking, are still successful \(t\) months later can be approximated by $$ P(t)=21.4(0.914)^{t} $$ Sources: New England Journal of Medicine; data from California's Smokers' Hotline a) Estimate the percent of smokers receiving telephone counseling who are successful in quitting for 1 month, 3 months, and 1 year. b) Graph the function.
Problem 53
Find the distance between each pair of points. \((-3,7)\) and \((-2,6)\)
Problem 53
Use a calculator to find each of the following rounded to four decimal places. $$ \text { 53. } 10^{2.3} $$
Problem 54
Solve The percent of smokers \(P(t)\) who, without telephone counseling, have successfully quit smoking for \(t\) months (see Exercise 53 ) can be approximated by $$ P(t)=9.02(0.93)^{t} $$ Sources: New England Journal of Medicine; data from California's Smokers' Hotline a) Estimate the percent of smokers not receiving telephone counseling who are successful in quitting for 1 month, 3 months, and 1 year. b) Graph the function.
