Answer
$f(x)=\displaystyle \frac{2}{3}(3^{x})$
Work Step by Step
Exponential models have form: $f(x)=y=Ab^{x}$
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Given
$f(1)=2\Rightarrow\quad 2=Ab^{1},$
Given
$f(3)=18\Rightarrow\quad 18=Ab^{3},$
Dividing the second equation with the first,
$\displaystyle \frac{18}{2}=\frac{Ab^{3}}{Ab}$
$9=b^{2}\Rightarrow b=3$
Back-substitute: $2=A(3^{1})\displaystyle \Rightarrow A=\frac{2}{3}$
Thus,
$f(x)=\displaystyle \frac{2}{3}(3^{x})$
