Answer
$y=1.3867\left(1.4422^{x}\right)$
Work Step by Step
The exponential function we want has the form $y=Ab^{x}$.
$\left[\begin{array}{ll}
\text{point on} & \text{corresponding}\\
\text{the graph} & \text{equation}\\
(1,2) & 2=Ab^{1}\\
(4,6) & 6=Ab^{4}
\end{array}\right]$
Dividing the equations,
$\displaystyle \frac{6}{2}=\frac{Ab^{4}}{Ab^{1}}$
$3=b^{2}$, so
$b=\sqrt{3}\approx 1.4422$
Back-substituting into the second equation,
$2=A(1.4422)^{1}$
$A=\displaystyle \frac{2}{1.4422}\approx 1.3867$
The model is
$y=Ab^{x}=1.3867\left(1.4422^{x}\right)$
