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:

$e^{-0.4x}=\dfrac{300}{1500},\\ \\e^{-0.4x}=\dfrac{1}{5},\\ \\-0.4x=\ln \dfrac{1}{5},\\ \\x=\dfrac{\ln \dfrac{1}{5}}{-0.4}\approx 4.024.$

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