Question

The function P(n) = 10*2^n/4 models the population of tree frogs living in a park after n months. How many months will it take for the tree frog population to reach 5120? Show your work.

Answer 1

They've given us a P value, so we just need to plug it into our function and find the corresponding n value:

`5120=10(2^{(n)/(4)})`

`512=2^{(n)/(4)}`

Then take the natural log of both sides:

`\ln(512)=\ln(2^{(n)/(4)})=(n)/(4)\ln(2)`

`(\ln(512))/(\ln(2))=(n)/(4)`

`4*(\ln(512))/(\ln(2))=n`

Putting this into a calculator:

`n=36`