Respuesta :
Answer:
13.79 hours
Explanation:
The decay model for the medication is:
[tex]M=400\left(0.86\right)^t[/tex]When the initial amount decreases to 50 mg:
[tex]50=400\left(0.86\right)^t[/tex]We then solve the equation for t:
[tex]\begin{gathered} \text{ Divide both sides by 400} \\ \frac{50}{400}=\frac{400}{400}\left(0.86\right)^t \\ \frac{1}{8}=0.86^t \\ 0.125=0.86^t \\ \text{ Take the log of both sides} \\ \log(0.125)=\log(0.86^t) \\ \operatorname{\log}(0.125)=t\operatorname{\log}(0.86) \\ \text{ Divide both sides by }\log0.86 \\ \frac{\begin{equation*}t\operatorname{\log}(0.86)\end{equation*}}{\operatorname{\log}(0.86)}=\frac{\operatorname{\log}(0.125)}{\operatorname{\log}(0.86)} \\ t\approx13.79\text{ hours} \end{gathered}[/tex]It will take 13.79 hours for the initial 400 mg of medicine to decrease to 50 mg.
