Chapter 2.3, Problem 62E

Medication in the bloodstream. After an injection, the amount of a medication A, in cubic centimeters (cc), in the bloodstream decreases with time t, in hours. Suppose that under certain conditions A is given by

$A\left(t\right)=\frac{A_0}{t^2+1},$

where $A_0$ is the initial amount of the medication. Assume that an initial amount of 100 cc is injected.

a. Find $A\left(0\right),A\left(1\right),A\left(2\right),A\left(7\right),\text{and }A\left(10\right)$.

b. Find the maximum amount of medication in the bloodstream over the interval $\left[0,\infty \right)$

c. Graph the function.

d. d) According to this function, does the medication ever completely leave the bloodstream? Explain your answer.