Question

In a town whose population is ​3800, a disease creates an epidemic. The number of people N infected t days after the disease has begun is given by the function N(t) = 3800/1+24.9e^-0.6t. Complete parts​ a) through​ c) below.

Answer 1

The mathematical problem relates to the exponential growth of an epidemic within a town of 3800 individuals, modeled by an exponential growth function. It provides insight into how the disease spreads over time and how the number of infected individuals approaches the town's total population.

Step-by-step explanation:

The question presented is a mathematical problem that involves an exponential growth function. The number of people infected N(t) with a disease in a town of 3800 people t days after the disease has begun is modeled by the function N(t) = 3800/1+24.9e^-0.6t.

As the equation shows, the number of infected individuals can be determined for any given day t, and the model predicts how the infection spreads over time. This is consistent with the concept that in epidemic situations, a population may experience rapid growth initially, followed by a slowdown as resources become scarce or interventions are made (reflective of a logistic growth model).

The function depicts exponential decay of the denominator term as time increases, which implies that initially, when t is small, the number of infected individuals will grow rapidly. However, as time goes on and the value of e^-0.6t decreases, the growth rate will slow down, and the population of infected individuals will approach the upper limit of 3800, the total population of the town.