Use the logistic growth model $f(x)=\frac{230}{1+5 e^{-2 x}}$.

Find $f(0)$. Round to the nearest tenth.

Interpret $f(0)$.
$f(0)$ represents the carrying capacity.
$f(0)$ represents the final amount.
$f(0)$ represents the rate of growth.
$f(0)$ represents the initial amount.
$f(0)$ represents the half life.

Answer

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Answer

Final Answer: $f(0)$ is $\boxed{38.3}$ and it represents the initial amount.

Steps

Step 1 ：Use the logistic growth model $f(x)=\frac{230}{1+5 e^{-2 x}}$.

Step 2 ：Find $f(0)$.

Step 3 ：Calculate $f(0)$ by substituting $x = 0$ into the equation, which gives $f(0) = \frac{230}{1+5 e^{0}}$.

Step 4 ：Calculate the value of $f(0)$ to get $f(0) = 38.333333333333336$.

Step 5 ：Round $f(0)$ to the nearest tenth to get $f(0) = 38.3$.

Step 6 ：Interpret $f(0)$. In the context of the logistic growth model, $f(0)$ represents the initial amount.

Step 7 ：Final Answer: $f(0)$ is $\boxed{38.3}$ and it represents the initial amount.