Chapter 5.6, Problem 9E

An Epidemic Model A certain disease is contracted in a population at an average age of $A_0$ if no one is immunized at birth. If $q$ percent of the population is immunized at birth, then the average age at which the disease is contracted is $A\left(q\right)$. One model gives the relation.

$A\left(q\right)=\frac{100A_0}{100-q}$

a What value of $q$ gives a pole for this rational function?

b. Explain in practical terms what happens to $A\left(q\right)$ when $q$ is near the pole.