Answer
$f(x)=3(2^{x})$
Work Step by Step
The given curve in the question passing through the points (1, 6) and (3, 24).
Therefore,
$f(1)=Cb^{1}=6$
$f(3)=Cb^{3}=24$
Further,
$\frac{f(3)}{f(1)}=\frac{Cb^{3}}{Cb^{1}}=\frac{24}{6}$
This implies
$b^{2}=4$
$b=2$
Also,
$Cb^{1}=6$
Thus, $C=\frac{6}{b}$
Plug 2 for $b$.
$C=\frac{6}{2}=3$
Hence, the required exponential function is $f(x)=3(2^{x})$.
