Answer
$y= \frac{1}{2} e^{\frac{\ln 10}{5}t}$
Work Step by Step
Use the two given points $(0,\frac{1}{2})$, and $(5,5)$
And the exponential function $y=Ce^{kt} $
Find C
$\frac{1}{2} = Ce^0 $
$ C=\frac{1}{2}$
$y=\frac{1}{2}e^{kt}$
Plug in (5,5)
$5=\frac{1}{2}e^{5t}$
$\ln {10} = 5t$
$t=\frac{\ln {10}}{5}$
$y= \frac{1}{2} e^{\frac{\ln 10}{5}t}$
