Question

Section 2.4 question: 3A certain community consists of 4500 people, and one individual has a particularly contagious strain of influenza. Assuming the community has not had vaccination shots and are all susceptible, the spread of the disease in the community is modeled byA=4500/1+4499e^−0.5t where A is the number of people who have contracted the flu after t days.(a) How many people have contracted the flu after 6 days? Round your answer to the nearest whole number. people(b) What is the carrying capacity for this model?(c) How many days will it take for 350 people to contract the flu? Round your answer to the nearest whole number. days.

Answer 1

Step 1:

In this question, we have the following:

Step 2:

a) How many people have contracted the flu after 6 days? We are meant to round our answer to the nearest whole number:

`\begin{gathered} A\text{ = }(4500)/(1+4499e^(-0.5t)) \\ \text{when }t=\text{ 6, we have that:} \end{gathered}`

A = 20 people ( to the nearest whole number)

Step 3:

b) What is the carrying capacity of the model?

`\begin{gathered} A\text{ =}\frac{4500\text{ }}{1+4499e^(-0.5t)} \\ \text{When t = }\infty\text{ , we have that:} \\ A\text{ = }(4500)/(1+0) \\ A\text{ =}(4500)/(1) \\ A\text{ = }4500\text{ } \end{gathered}`

The graph of the carrying capacity is as shown below:

The carrying capacity = 4500

Step 4:

How many days will it take 350 people to contract the flu?

Round the answer to the nearest whole number.

The graph of the solution is as shown below:

From the graph, we can see clearly that when there are 350 people,

it will take:

`\begin{gathered} 11.877\text{ days} \\ \approx\text{ 12 days ( to the nearest whole number )} \end{gathered}`

CONCLUSION: It will take 12 days for 350 people to contract the flu.