Answer
$f(x)=\displaystyle \frac{10}{1+4(0.8)^{-x}}$
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
$\left\{\begin{array}{l}
N=10,\\
b=0.8,\\
\dfrac{N}{1+A}=2
\end{array}\right.$
We plug this in to obtain:
$\displaystyle \frac{N}{1+A}=2 \quad\Rightarrow\left\{\begin{array}{ll}
\dfrac{10}{1+A} & =2\\
\dfrac{10}{2} & =1+A\\
5-1 & =A\\
A & =4
\end{array}\right.$
Thus we get:
$f(x)=\displaystyle \frac{10}{1+4(0.8)^{-x}}$
