Answer
$
f(x)=4.9497\cdot\left(1.4142\right)^x
$
Work Step by Step
The graph shows that the points $(1,7),(3,14)$ and $(5,28)$ lie on the curve of $f(x)$. If the graph of the function is exponential, then the ratios of successive values of $f(x)$ will be a constant.
$$
\begin{aligned}
& \frac{f(3)}{f(1)}=\frac{14}{7}=2 \\
& \frac{f(5)}{f(3)}=\frac{28}{14}=2.
\end{aligned}
$$
Clearly, the function is an exponential function. We now proceed to find an expression of the exponential function of the form, $f(x) = ab^x$.
$$
\begin{aligned}
\frac{f(3)}{f(1)} & =\frac{14}{7} \\
\frac{a b^3}{a b^1} & =2\\
b^2& = 2\\
b= \sqrt{2}\approx 1.4142
\end{aligned}
$$ We determine $a$:
$$
\begin{aligned}
ab^{1}& =7\\
a & =\frac{7}{b} \\
a & ==\frac{7}{\sqrt 2}\approx \frac{7}{1.4142}=4.9497
\end{aligned}
$$ It follows that
$$
f(x)=4.9497\cdot\left(1.4142\right)^x
$$
