91Ó°ÊÓ

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, graph the function and its reflection about the \(x\) -axis on the same axes. $$ f(x)=\frac{1}{2}(4)^{x} $$

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

For the following exercises, use logarithms to solve. $$ 10 e^{8 x+3}+2=8 $$

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

The formula for an increasing population is given by \(P(t)=P_{0} e^{r t}\) where \(P_{0}\) is the initial population and \(r>0\). Derive a general formula for the time \(t\) it takes for the population to increase by a factor of \(M\).

For the following exercises, state the domain, range, and \(x\) -and \(y\) -intercepts, if they do not exist, write DNE. $$f(x)=\log _{2}(x+2)-5$$

For the following exercises, rewrite each equation in logarithmic form. $$10^{a}=b$$

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 years will it take before there are 100 wolves in 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. How many years will it take before there are 100 wolves in the habitat?