Question

I’ve been trying to figure out how to solve this and was wondering how to do this correctly!

Answer 1

To solve this we will use the form for exponential growth to determine the formula to use.

Exponential growth has the form

`\begin{gathered} P=P_0e^(rt) \\ P=\text{population after timer t} \\ P_0=\text{ initial population growth } \\ r=\text{ percent growth rate} \end{gathered}`

Now the frogs tripple in population after 9 days. Initially they were 21. So in 9 days they become

`21*3=63\text{ frogs }`

Applying the formula, we have

`\begin{gathered} P=P_0e^(rt) \\ 63=21e^(9r) \\ 3=e^(9r) \\ \text{taking ln of both sides } \\ \ln 3=\ln e^(9r) \\ \ln 3=9r \\ r=(\ln3)/(9) \end{gathered}`

The time for the frogs to get to 290 becomes