Answer
$(A)$
Work Step by Step
Goal: $\displaystyle \quad f(x)=\frac{N}{1+Ab^{-x}}$,
where $N$ = limiting value = about $7$ (B and C are eliminated).
Cases A and D both have A=5.4, so we don't observe $f(0)$.
The graph is rising, so $b\gt 1,$ and cases A and D both have this.
We have a choice of $b$ being either $1.2$ or $6.2$.
Since f(x) is roughly exponential for small x, and we have for $x=0$, the value $f(0)\approx 1$.
Increasing x by 1 (from 0 to 1), we expect $f(x)$ to rise by the factor $b.$ The graph suggests a factor of $1.2$ rather than $6.2$, (approximating $f(1)$, the value is about 1.5), so our choice is $(A)$.
