Answer
$y= \dfrac{1}{2} e^{\frac{x}{4}\ln 10}$
Work Step by Step
We have $y=ae^{bx}$
Set $(x,y)= (0, \dfrac{1}{2})$
So, $\dfrac{1}{2}=ae^{b(0)} \implies a=\dfrac{1}{2}$
Further, we have $y=ae^{bx}$
Set $(x,y)= (4,5)$ to compute $b$
So, $5=\dfrac{1}{2} e^{4b} \implies e^{4b}=10$
and $\ln 10 =\ln 4b \implies b =\dfrac{1}{4} \ln 10$
Now, the exponential decay model is: $y= \dfrac{1}{2} e^{\frac{x}{4}\ln 10}$
