91Ó°ÊÓ

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 initial population of fish?

Use this scenario: The population \(P\) of a koi pond over \(x\) months is modeled by the function \(P(x)=\frac{68}{1+16 e^{-0.28 x}}\). How many koi will the pond have after one and a half years?

For the following exercises, rewrite each equation in logarithmic form. $$ m^{-7}=n $$

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 initial population of fish?

For the following exercises, use logarithms to solve. $$ -5 e^{9 x-8}-8=-62 $$

For the following exercises, condense to a single logarithm if possible. $$ \ln \left(y \sqrt{\frac{y}{1-y}}\right) $$

For the following exercises, find the formula for an exponential function that passes through the two points given. $$ (0,6) \text { and }(3,750) $$

For the following exercises, state the domain, vertical asymptote, and end behavior of the function. $$h(x)=-\log (3 x-4)+3$$

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 \(P(t)=\frac{1000}{1+9 e^{-0.6 t}} .\) To the nearest tenth, what is the doubling time for the fish population?

For the following exercises, condense to a single logarithm if possible. $$ \log \left(x^{2} y^{3} \sqrt[3]{x^{2} y^{5}}\right) $$