In Example 8, we modeled a measles pathogenesis curve by a...

In Example 8, 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 8, on what day does this occur? (b) Let $P_3$ be the point on the graph of $g$ where infectiousness begins. 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 8(b). On what day does infectiousness end? (c) Compute the level of infectiousness for this patient.

In Example 8, 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 8, on what day does this occur?
(b) Let $P_3$ be the point on the graph of $g$ where infectiousness begins. 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 8(b). On what day does infectiousness end?
(c) Compute the level of infectiousness for this patient.

Transcript

00:02 In this question, we're asked to, given a model for the contagiousness of a disease, we want to find out a couple of things about this disease, considering a patient with measles.

00:16 Now, i know that the patient with measles has his pathogenesis modeled by a separate function, and we want to find out where, in this case, the infectiousness starts.

00:27 So what i did was i drew a graph using wolfram alpha, and i want to find the intersection point between this measles graph and the first sign of infectiousness.

00:41 The first sign of infectiousness is 1210.

00:44 So where does g of t equal 1210? and since the t is in days, we get that t is going to be approximately, i used a graph and calculator for this.

01:05 You can too.

01:06 It appears to be about 11 .258.

01:13 But since we don't want to work with decimal days, we're going to round that off to 12 days.

01:25 The next part of this asks us, when does it end? in this case, we want below.

01:40 We want to have the second point below where it's basically where the graph touches 1210 a second time.

02:01 So from that, we can find out where else is g of t equal to 1210.

02:13 And if we again look at the graph in utility, we're going to have that this is approximately going to be 17 .18, which we will again round to 18 days.

02:37 Finally, for the last step, we want to find out how much infectiousness he has...

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