Answer
$f(x)= (10)^x$
Work Step by Step
Let $f(x)=a b^x$. We know from the graph that $f(0)=a b^0= a=1$ and $f(2)= b^{2}=100$. So
$$
\begin{aligned}
100 & =(1) b^2 \\
b^2 & =100 \\
b=10 & \text { or } b=-10
\end{aligned}
$$ As $f$ is increasing, we have:
$$f(x)= (10)^x$$
