SOLUTION:
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:
[tex]\begin{gathered} A\text{ = }\frac{4500}{1+4499e^{-0.5t}} \\ \text{when }t=\text{ 6, we have that:} \end{gathered}[/tex]
A = 20 people ( to the nearest whole number)
Step 3:
b) What is the carrying capacity of the model?
[tex]\begin{gathered} A\text{ =}\frac{4500\text{ }}{1+4499e^{-0.5t}} \\ \text{When t = }\infty\text{ , we have that:} \\ A\text{ = }\frac{4500}{1+0} \\ A\text{ =}\frac{4500}{1} \\ A\text{ = }4500\text{ } \end{gathered}[/tex]
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:
[tex]\begin{gathered} 11.877\text{ days} \\ \approx\text{ 12 days ( to the nearest whole number )} \end{gathered}[/tex]
CONCLUSION: It will take 12 days for 350 people to contract the flu.
