Answer
about 11 years
Work Step by Step
Exponential growth and decay models are given by $A=A_{0}e^{kt}$
in which $t$ represents time,
$A_{0}$ is the amount present at $t=0$, and
$A$ is the amount present at time $t$.
If $k>0$, the model describes growth and $k$ is the growth rate.
If $k<0$, the model describes decay and $k$ is the decay rate
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We have a decay model, and we want to find
the time t in which A becomes $0.5A_{o}$:
$0.5=e^{-0.063t} \displaystyle \qquad .../\times\frac{1}{A_{o}}$
$0.5=e^{-0.063t}\qquad .../$ take ln( ) of both sides
$\ln 0.5=-0.063t\qquad .../\div(-0.063)$
$ t=\displaystyle \frac{\ln 0.5}{-0.063}\approx$11.0023361994
The half-life is about 11 years.
