Answer
$y_{3}=by_{2}$
$y_{3}=b^{2}y_{1}$,
where $b$ is the common ratio $b=\displaystyle \frac{y_{2}}{y_{1}}= \displaystyle \frac{y_{3}}{y_{2}} $
Work Step by Step
An exponential curve is the graph of a function of the form
$y=f(x)=Ab^{x}$
The ratio
$\displaystyle \frac{f(x+1)}{f(x)}=\frac{Ab^{x+1}}{Ab^{x}}=b$
tells us that
$\displaystyle \frac{y_{2}}{y_{1}}$ and $\displaystyle \frac{y_{3}}{y_{2}} $ should be the same (equal to a number $b)$ in order for the points to lie on the curve.
Then,
$y_{2}=by_{1}$
and
$y_{3}=by_{2}=b(by_{1})=b^{2}y_{1}$
