# How could the graph of an exponential function be used to determine an a value?

I assume you mean the "A" as in the initial value of $y = A {e}^{r t}$? $y$-intercept
The "a" value occurs at $t = 0$, so ${e}^{0} = 1$, therefore $y = A$ is $\left(0 , A\right)$, the $y$-intercept.