Question

How long will it take for the population to reach 3042 fish, according to this model?

Answer 1

We have an exponential growth model for the fish population, where P(t) is the population and t is the time in years:

`P(t)=338(3)^{(t)/(3)}`

We have to calculate the time t for which the population is P = 3042.

We start from P(t) = 3042 and rearrange the equation to find the value of t:

`\begin{gathered} P(t)=3042 \\ 338(3)^{(t)/(3)}=3042 \\ 3^{(t)/(3)}=(3042)/(338) \\ 3^{(t)/(3)}=9 \\ (t)/(3)\ln(3)=\ln(9) \\ (t)/(3)=(\ln(9))/(\ln(3)) \\ (t)/(3)=2 \\ t=2*3 \\ t=6 \end{gathered}`

Answer: after t = 6 years, the population will be 3042.