Chapter 3 - Section 3.5 - Exponential Growth and Decay; Modeling Data - Exercise Set - Page 506: 22

$11.0$ years

Model: $ A=A_{0}e^{kt}$ Unknown: $ t $, when $ A=0.5A_{0},\ k=-0.063$ $0.5A_{0}=A_{0}e^{-0.063t}\qquad... /\div A_{0}$ $0.5=e^{-0.063t}\qquad.../\ln(...)$ $-0.693147=-0.063t\qquad.../\div(-0.063)$ $ t\approx 11.0$ years