Chapter 6 - Inverse Functions - 6.5 Exponential Growth and Decay - 6.5 Exercises - Page 472: 7

a) $y(t)$ = $Ce^{-0.0005t}$ b) $211$ s

a) If $y$ = $[N_2O_5]$, then by Theorem which states that the only solutions of the differential equation $dy/dt = ky$ are the exponential functions $y(t)=y(0)e^{kt}$, we have: $\frac{dy}{dt}$ = $-0.0005y$ $y(t)$ = $y(0)e^{-0.0005t}$ = $Ce^{-0.0005t}$ b) $y(t)$ = $Ce^{-0.0005t}$ = $0.9C$ $Ce^{-0.0005t}$ = $0.9C$ $e^{-0.0005t}$ = $0.9$ $-0.0005t$ = $\ln0.9$ $t$ $\approx$ $211$ s