Answer
$y=2.1213\left(1.4142^{x}\right)$
Work Step by Step
The exponential function we want has the form $y=Ab^{x}$.
$\left[\begin{array}{ll}
\text{point on} & \text{corresponding}\\
\text{the graph} & \text{equation}\\
(1,3) & 3=Ab^{1}\\
(3,6) & 6=Ab^{3}
\end{array}\right]$
Dividing the equations,
$\displaystyle \frac{6}{3}=\frac{Ab^{3}}{Ab^{1}}$
$2=b^{2}$, so
$b=\sqrt{2}\approx 1.4142$
Back-substituting into the second equation,
$3=A(1.4142)^{1}$
$A=\displaystyle \frac{3}{1.4142}\approx 2.1213$
The model is
$y=Ab^{x}=2.1213\left(1.4142^{x}\right)$