91Ó°ÊÓ

For the following exercises, condense each expression to a single logarithm using the properties of logarithms. $$ 2 \log (x)+3 \log (x+1) $$

Use this scenario: The population \(P\) of an endangered species habitat for wolves is modeled by the function \(P(x)=\frac{558}{1+54.8 e^{-0.462 x}},\) where \(x\) is given in years. What was the initial population of wolves transported to the habitat?

For the following exercises, use this scenario: The population \(P\) of an endangered species habitat for wolves is modeled by the function \(P(x)=\frac{558}{1+54.8 e^{-0.42 x}},\) where \(x\) is given in years. What was the initial population of wolves transported to the habitat?

Use a graphing calculator and this scenario: the population of a fish farm in \(t\) years is modeled by the equation \(P(t)=\frac{1000}{1+9 e^{-0.6 t}}.\) What is the carrying capacity for the fish population? Justify your answer using the graph of \(P.\)

For the following exercises, use a graphing calculator and this scenario: the population of a fish farm in \(t\) years is modeled by the equation \(P(t)=\frac{1000}{1+9 e^{-0.6 t}} .\) What is the carrying capacity for the fish population? Justify your answer using the graph of \(P\).

A substance has a half-life of 2.045 minutes. If the initial amount of the substance was 132.8 grams, how many half-lives will have passed before the substance decays to 8.3 grams? What is the total time of decay?

For the following exercises, use this scenario: The population \(P\) of an endangered species habitat for wolves is modeled by the function \(P(x)=\frac{558}{1+54.8 e^{-0.42 x}},\) where \(x\) is given in years. How many wolves will the habitat have after 3 years?

For the following exercises, rewrite each equation in logarithmic form. $$y^{x}=\frac{39}{100}$$

For the following exercises, state the domain, range, and \(x\) -and \(y\) -intercepts, if they do not exist, write DNE. $$g(x)=\ln (-x)-2$$

Use this scenario: The population \(P\) of an endangered species habitat for wolves is modeled by the function \(P(x)=\frac{558}{1+54.8 e^{-0.462 x}},\) where \(x\) is given in years. . How many wolves will the habitat have after 3 years?