Answer
See an explanation
Work Step by Step
$A(t)=A_{0}e^{kt},$
$A_{0}$ is the Initial amount.
$k$ is negative number.
a. From the formula $A(t)=A_{0}e^{-0.0244t},$ Whereas $A_0$ is the Initial amount and $A(t)$ is the amount remaining after $t$ years. The decay rate is, $k=-0.0244.$
b.$A(10)=500e^{-0.0244\times 10}=391.744,$
c.
$A(t)=500e^{-0.0244t}=400,$
$e^{-0.0244t}=0.8,$
$-0.0244t=\ln{0.8},$
$t=9.15,$
d.
$A(t)=500e^{-0.0244t}=250,$
$e^{-0.0244t}=0.5,$
$-0.0244t=\ln{0.5},$
$t=28.41$
