Use a graphing calculator and the following scenario.
The population $P$ of a fish farm in $t$ years is modeled by the equation $P(t)=\frac{1400}{1+9 e^{-0.9 t}}$. To. the nearest tenth, how long will it take for the population to reach 900 ?
Answer
The real solution is approximately 3.094 years. Therefore, it will take approximately \(\boxed{3.1}\) years for the population to reach 900.
Step 1 ：The population $P$ of a fish farm in $t$ years is modeled by the equation $P(t)=\frac{1400}{1+9 e^{-0.9 t}}$. We are asked to find how long it will take for the population to reach 900. This means we need to solve the equation $P(t)=900$ for $t$.
Step 2 ：Setting $P(t)=900$ and solving for $t$ gives several solutions. However, only the real number solution is meaningful in this context, as time cannot be a complex number.
Step 3 ：The real solution is approximately 3.094 years. Therefore, it will take approximately \(\boxed{3.1}\) years for the population to reach 900.
