Chapter 4 - 4.1 Introduction to the Family of Exponential Functions - Exercises and Problems for Section 4.1 - Exercises and Problems - Page 147: 52

a) 25 mg b) $15\%$ c) 4.92 mg d) About 20 hours.

Given $$A(t) =25\cdot (0.85)^{t} $$ A) The initial dose is $25$ mg. B)The percentage of the drug leaving the body is $r= 1-0.85 = 0.15= 15\%$. C) \begin{equation} \begin{aligned} y&=25\cdot (0.85)^{10}\\ &= 4.92\\ \end{aligned} \end{equation} D) Use $t=\log_{0.85}(A(t)/25)$ \begin{equation} \begin{aligned} t&=\log_{0.85}(A(t)/25)\\ &= \log_{0.85}(1/25)\\ &= 19.80 \end{aligned} \end{equation} About 20 hours.