Question

The total number of people infected with a virus often grows like a logistic curve. Suppose that 10 people originally have the virus, and that in the early stages of the virus (with time, t, measured in weeks), the number of people infected is increasing exponentially with k=2. It is estimated that, in the long run, approximately 4750 people become infected. Use this information to find a logistic function to model this situation.

Answer 1

To model the situation, we can use a logistic function: P(t) = 4750 / (1 + A * e^-2t).

Step-by-step explanation:

To model the situation of the total number of people infected with a virus, we can use a logistic function.

A logistic function is of the form: P(t) = K / (1 + A * e-kt), where P(t) is the number of infected people at time t, K is the carrying capacity (the maximum number of infected people), A is a constant that determines the initial growth rate, and k is a constant that determines the rate of growth.

In this case, we are given that the number of infected people is increasing exponentially with k = 2. We are also given that the long-term number of infected people is approximately 4750. Using this information, we can write the logistic function as: P(t) = 4750 / (1 + A * e-2t).