91Ó°ÊÓ

Use this scenario: The population \(P\) of a koi pond over \(x\) months is modeled by the function \(P(x)=\frac{68}{1+16 e^{-0.28 x}}\). What was the initial population of koi?

For the following exercises, use logarithms to solve. $$ e^{-3 k}+6=44 $$

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 \(P(t)=\frac{1000}{1+9 e^{-0.6 t}} .\) Graph the function.

For the following exercises, condense to a single logarithm if possible. $$ \log \left(\sqrt{x^{3} y^{-4}}\right) $$

For the following exercises, state the domain, vertical asymptote, and end behavior of the function. $$f(x)=\log \left(x-\frac{3}{7}\right)$$

Use a graphing calculator and this scenario: the population of a fish farm in \(t\) years is modeled by the equation \(P(t)=\frac{1000}{1+9 e^{-0.6 t}}.\) Graph the function.

For the following exercises, use the properties of logarithms to expand each logarithm as much as possible. Rewrite each expression as a sum, difference, or product of logs. $$ \log \left(\sqrt{x^{3} y^{-4}}\right) $$

For the following exercises, rewrite each equation in logarithmic form. $$ c^{d}=k $$

For the following exercises, determine whether the equation represents exponential growth, exponential decay, or neither. Explain. $$ y=11,701(0.97)^{t} $$

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?