Chapter 6.1, Problem 51E

In Example 5, we modeled a measles pathogenesis curve by a function f. A patient infected with the measles virus who has some immunity to the virus has a pathogenesis curve that can be modeled by, for instance, g(t) = 0.9f(t).

(a) If the same threshold concentration of the virus is required for infectiousness to begin as in Example 5, on what day does this occur?

(b) Let P₃ be the point on the graph of g where infectiousness begins. It has been shown that infectiousness ends at     a point P₄ on the graph of g where the line through P₃, P₄ has the same slope as the line through P₁, P₂ in Example 5(b). On what day does infectiousness end?

(c) Compute the level of infectiousness for this patient.