Answer
$f(x)=\displaystyle \frac{25}{1+4(1.1)^{-x}}$
Work Step by Step
Logistic model: $f(x)=\displaystyle \frac{N}{1+Ab^{-x}}$,
where $N$ = limiting value.
While x is relatively small, $f$ behaves exponentially,
$f(x)\displaystyle \approx(\frac{N}{1+A})b^{x}.$
We are given
$\left\{\begin{array}{l}
N=25,\\
b=1.1,\\
\dfrac{N}{1+A}=5
\end{array}\right.$
We plug this in to obtain:
$\dfrac{N}{1+A}=5\quad\Rightarrow\left\{\begin{array}{ll}
\dfrac{25}{1+A} & =5\\
\dfrac{25}{5} & =1+A\\
5-1 & =A\\
A & =4
\end{array}\right.$
Thus, we get:
$f(x)=\displaystyle \frac{25}{1+4(1.1)^{-x}}$
