10. Measles pathogenesis If a patient has had previous

exposure to measles, the immune system responds more

quickly. This results in a suppression of the level of virus in

the plasma during an infection. Suppose that such previous

exposure causes the viral density in the plasma to be $\frac{3}{5}$ of

that in a patient with no previous exposure. This means that

the level of virus in the plasma is given by $\frac{3}{5} f(t),$ where

$f(t)=-t(t-21)(t+1)$ as in Exercise $9 .$

$$\begin{array}{l}{\text { (a) Use subintervals of width } 2 \text { days and their midpoints to }} \\ {\text { estimate the total amount of infection at } t=12 \text { days. }} \\ {\text { (b) If } 7848 \text { cells per mL } x \text { days is the total amount of }} \\ {\text { infection required to develop symptoms, use subinter- }} \\ {\text { vals of width } 2 \text { days and their midpoints to estimate the }} \\ {\text { day when symptoms will appear. }}\end{array}$$

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