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15 votes
15 votes
Use logarithms to find the how long it would take for your body to only have 50mg of caffeine remaining in your system. Show all your work.

User Silverlight Student
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1 Answer

22 votes
22 votes

The function that describes the situation is:


C(t)=100e^(-0.17t)

Where C represents the caffeine remaining, and t represents the time.

We want to find t such that C(t)=50. So,


50=100e^(-0.17t)

To solve this equation for t, we could use logarithms as follows:


\begin{gathered} 50=100e^(-0.17t) \\ (50)/(100)=e^(-0.17t) \\ 0.5=e^(-0.17t) \\ \ln (0.5)=\ln (e^(-0.17t)) \\ \ln (0.5)=-0.17t \\ (\ln (0.5))/(-0.17)=t \\ 4.08=t \end{gathered}

Therefore, it would take 4.08 hours for your body to have only 50mg of caffeine remaining.

User Prasad Weera
by
3.1k points
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