The function [tex]P(x)=1500e^{-0.4x}[/tex] gives the number of the original trout alive after x years. When the number of the original trout alive is 300, then
[tex]300=1500e^{-0.4x}[/tex]
Solve this equation:
[tex]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.[/tex]
Answer: after 4.024 year (or 5 year if round to the whole number of years)
