Question

A lake is stocked with 1,500 young trout. If the number of the original trout alive after x years is given by the function P(x)=1500e^-0.4x, when will there be 300 of the original trout left?

Answer 1

The function
`P(x)=1500e^(-0.4x)` gives the number of the original trout alive after x years. When the number of the original trout alive is 300, then

`300=1500e^(-0.4x)`

Solve this equation:

`e^(-0.4x)=(300)/(1500),\\ \\e^(-0.4x)=(1)/(5),\\ \\-0.4x=\ln (1)/(5),\\ \\x=(\ln (1)/(5))/(-0.4)\approx 4.024.`

Answer: after 4.024 year (or 5 year if round to the whole number of years)