Question

the function ( n(t)=\frac{70,000}{1 + 40e^{-2.5t}} ) describes the number of people, ( n(t) ), who become ill with a virus ( t ) weeks after its initial outbreak in a town with 70,000 inhabitants. the horizontal asymptote in the graph indicates that there is a limit to the epidemics growth. complete parts (a) through (c) below. c. why cant the spread of an epidemic simply grow indefinitely? a. a treatment for the virus is eventually found. b. all the ill people die from the virus. c. the number of ill people cannot exceed the population of the town. d. the people of the town gradually develop an immunity to the virus. e. all of the above.

Explanation:

The function \(N(t)=\frac{70000}{1 + 40e^{-2.5t}}\) models the number of ill people. The town has a fixed population of \(70000\). Logically, the number of ill people can't surpass the total population. Option A assumes a treatment is found, but the function doesn't rely on that. Option B is extreme as not all ill people necessarily die. Option D about immunity isn't indicated by the function. Since the population is a hard - limit, Option C is correct.

Answer:

C. The number of ill people cannot exceed the population of the town.