Question

A lake is stocked with 20 carp. If the carp population grows at a rate of 7.5% per month, when will the pond contain 500 carp? Round your answer to the nearest hundredth.

Answer 1

We have a lake with 20 carp and a gowth rate of 7.5% per month, so the equation of the population at time t is:

So, we need to find the value of t when P(t)=500 and P0 (the initial population) is 20:

`\begin{gathered} P(t)=500=20\cdot(1+(7.5)/(100))^t \\ (500)/(20)=1.075^t \\ \log (25)=\log (1.075^t) \\ \log (25)=t\cdot\log (1.075) \\ t=(\log(25))/(\log(1.075))=44.51 \end{gathered}`

The lake contain 500 carp in 44.51 months.