Answer
a) $\approx$ $13$ years
b) $\approx$ $29$ years
Work Step by Step
a)
$y(t)$ = $y(0)e^{-kt}$
$y(1)$ = $y(0)e^{-k}$
$0.945y(0)$ = $y(0)e^{-k}$
$k$ = $0.057$
$y(t)$ = $y(0)e^{-0.057t}$
Half life
$\frac{1}{2}y(0)$ = $y(0)e^{-0.057t}$
$\frac{1}{2}$ = $e^{-0.057t}$
$t$ $\approx$ $12.25$ years $\approx$ $13$ years
b)
$y(t)$ = $y(0)e^{-0.057t}$
$0.2y(0)$ = $y(0)e^{-0.057t}$
$0.2$ = $e^{-0.057t}$
$t$ $\approx$ $28.45$ years $\approx$ $29$ years