#### Answer

about 12.6 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
-----------
We have a decay model, and we want to find
the time t in which A becomes $0.5A_{o}$
$0.5A_{o}=A_{o}e^{-0.055t} \displaystyle \qquad .../\times\frac{1}{A_{o}}$
$0.5=e^{-0.055t}\qquad .../$ take ln( ) of both sides
$\ln 0.5=-0.055t\qquad .../\div(-0.055)$
$ t=\displaystyle \frac{\ln 0.5}{-0.055}\approx$12.6026760102
The half-life is about 12.6 years.