Problem

Use a graphing calculator and the following scenario. The population $P$ of a fish farm in $t$ years is modeled by the equation $P(t)=\frac{1400}{1+9 e^{-0.7 t}}$. To the nearest. whole number, what will the fish population be after 2 years?

Solution

Step 1 :The population $P$ of a fish farm in $t$ years is modeled by the equation $P(t)=\frac{1400}{1+9 e^{-0.7 t}}$.

Step 2 :We are asked to find the fish population after 2 years. This means we need to find the value of $P(t)$ when $t=2$.

Step 3 :Substitute $t=2$ into the function to get $P(2)=\frac{1400}{1+9 e^{-0.7 \times 2}}$.

Step 4 :Calculate the value of $P(2)$ to get $P(2) \approx 434.86733010606594$.

Step 5 :Round $P(2)$ to the nearest whole number to get $\text{round}(P(2)) = 435$.

Step 6 :Final Answer: The fish population after 2 years will be approximately \(\boxed{435}\).

From Solvely APP
Source: https://solvelyapp.com/problems/18458/

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