Chapter 5 - 5.5 - Exponential and Logarithmic Models - 5.5 Exercises - Page 405: 5

(a) $P=Ae^{-rt}$ (b) $t=\ln\sqrt[r] {\frac{A}{P}}$

(a) $A=Pe^{rt}$ $P=\frac{A}{e^{rt}}=Ae^{-rt}$ (b) $A=Pe^{rt}$ $\ln A=\ln (Pe^{rt})$ $\ln A=\ln P+\ln e^{rt}$ $\ln A-\ln P=rt$ $\ln\frac{A}{P}=rt$ $t=\frac{1}{r}\ln\frac{A}{P}$ $t=\ln\sqrt[r] {\frac{A}{P}}$