Chapter 5.4, Problem 13E

Amount of a Drug in the Bloodstream After a drug is taken orally, the amount of the drug in the bloodstream after t hours is $f\left(t\right)=122\left(e^{-0.2t}-e^{-t}\right)$ units.

a. Graph $f\left(t\right),f\text{'}\left(t\right)$ and $f\text{'}\text{'}\left(t\right)$ in the window $\left[0,12\right]$ by $\left[-20,75\right]$.

b. How many units of the drug are in the bloodstream after $7$ hours?

c. At what rate is the level of drug in the bloodstream increasing after $1$ hour?

d. While the level is decreasing, when is the level of drug in the bloodstream $20$ units?

e. What is the greatest level of drug in the bloodstream, and when is this level reached?

f. When is the level of drug in the bloodstream decreasing the fastest?