Answer
$ 0.0152\%$ per year = $-0.000152$
Work Step by Step
Model: $ A=A_{0}e^{kt}$
Unknown: $ k $, when $ A=0.5A_{0},\ t=4560$
$0.5A_{0}=A_{0}e^{k\cdot 4560}\qquad... /\div A_{0}$
$0.5=e^{k\cdot 4560}\qquad.../\ln(...)$
$-0.693147=4560k\qquad.../\div(4560)$
$ k\approx-0.000152$
The decay rate is
$ 0.0152\%$ per year = $-0.000152$