Answer
$F(t)=4000\cdot(1.75)^{t/3}$
where $t=0$ is three years ago.
Work Step by Step
Let $t=0$ represent three years ago (the beginning).
Let $F(t)$ be the number of flies, $t$ years from the beginning.
We want an exponential model, $F(t)=Ab^{t}$
The initial value at $t=0 $ is $A=4000$
$(3,7000)$ - now - $\Rightarrow\left\{\begin{array}{l}
7000=4000 b^{3}\\
b^{3}=7000/4000\\
b^{3}=7/4\\
b=(1.75)^{1/3}
\end{array}\right.$
$F(t)=4000\cdot[(1.75)^{1/3}]^{t}$
$F(t)=4000\cdot(1.75)^{t/3}$
