Question

How long will it take for the population to get to 2552 alligators?

Answer 1

we have the equation

`P(t)=319(2)^{((t)/(3))}`

For P(t)=2,552

substitute in the given equation

`2,552=319(2)^{((t)/(3))}`

solve for t

`\begin{gathered} 2,552=319(2)^{((t)/(3))} \\ (2,552)/(319)=(2)^{((t)/(3))} \end{gathered}`

Apply log both sides

`\begin{gathered} \log \lbrack(2,552)/(319)\rbrack=\log \lbrack(2)^{((t)/(3))}\rbrack \\ \log \lbrack(2,552)/(319)\rbrack=(t)/(3)\cdot\log (2) \end{gathered}`

t=9 years

the answer is 9 years from the time of introduction