Question

The spread of a highly contagious virus in a high school can be described by the logistic function

g(x)=43/1+6.40e^−0.36x

where x is the number of days after the virus is identified in the school and​ g(x) is the total number of people who are infected by the virus.

​(a) How many students had the virus when it was first​ discovered?

​(b) Graph the function for

0≤x≤50.

​(c) Determine when the virus will infect

24 students.

​(d) According to this​ model, will the virus infection level off at any point in the​ future?

Answer 1

Answer:)

From the setup of the problem, we see that:

a.) When it was first discovered, x = 0. This means that the number of students infected when it was first discovered is given by :

Thus, roughly 6 people were infected when the virus was discovered.

b.) The graph of the function of the spread of the virus is as below:

c.) We want to figure out when g(x) = 24. For this, we can see where the line y = 24 intersects the graph of g(x) or we can solve for x in the equation :

From the graph also, we find that g(x) = 24 when x is roughly 5.805, which confirms our calculations.

d.) According to this model, the virus infection will level off in the future. We can see this behavior of g(x) in the graph as well, that is as x tends to very high values, g(x) tails to a constant value representing the fact that future infection levels will level off.

This value can be found in the limit as x tends to infinity:

Since the exponential in the denominator becomes very small as x tends to very large values.