## College Algebra (6th Edition)

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.