Problem

The population of a fish farm in $t$ years is modeled by the equation $P(t)=\frac{1250}{1+9 e^{-0.6 t}}$. Rounded to the nearest fish, what is the intial population?

Answer

Expert–verified
Hide Steps
Answer

Final Answer: The initial population of the fish farm is \(\boxed{125}\)

Steps

Step 1 :The population of a fish farm in $t$ years is modeled by the equation $P(t)=\frac{1250}{1+9 e^{-0.6 t}}$. We need to find the initial population, which is the population at time $t=0$.

Step 2 :Substitute $t=0$ into the equation to get $P(0)=\frac{1250}{1+9 e^{-0.6 \times 0}}$

Step 3 :Simplify the equation to get $P(0)=125.0$

Step 4 :Round $P(0)$ to the nearest fish to get $\text{round}(P(0)) = 125$

Step 5 :Final Answer: The initial population of the fish farm is \(\boxed{125}\)

link_gpt