13:52
Calculus: Early Transcendentals
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) = 0.9 f(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 $ P_3 $ be the point of the graph of $ g $ where infectiousness begin. It has been shown that infectiousness ends at a point $ P_4 $ on the graph of $ g $ where the line through $ P_3 $, $ P_4 $ has the same slope as the line through $ P_1 $, $ P_2 $ in Example 5(b). On what day does infectiousness end?
(c) Compute the level of infectiousness for this patient.