Answer
$\mathscr{E} = \frac{\pi~r^2~B_0}{\tau}~e^{-t/\tau}$
Work Step by Step
$B = B_0~e^{-t/\tau}$
$\frac{dB}{dt} = -\frac{B_0}{\tau}~e^{-t/\tau}$
We can find an expression for the emf in the loop:
$\mathscr{E} = -\frac{d\Phi}{dt}$
$\mathscr{E} = -A~\frac{dB}{dt}$
$\mathscr{E} = -(\pi~r^2)~(-\frac{B_0}{\tau}~e^{-t/\tau})$
$\mathscr{E} = \frac{\pi~r^2~B_0}{\tau}~e^{-t/\tau}$
