Question

In a town whose population is 3600, a disease creates an epidemic. The number of people N infected t days after the disease has begun is giving by the function *Picture* 3600N(t)= ———————- 1+18.7e^-0.4tFind the number of people infected after 8 days, (round to the nearest whole number)

Answer 1

2,043 peoples

Explanations:

Given the expression that determines the number of people N infected t days after the disease has begun shown below:

`N(t)=(3600)/(1+18.7e^(-0.4t))`

where:

t is the time (in days)

In order to determine the number of people infected after 8 days, we will substitute t = 8 into the function above to have;

`\begin{gathered} N(8)=(3,600)/(1+18.7e^(-0.4(8))) \\ N(8)=(3,600)/(1+18.7e^(-3.2)) \\ N(8)=(3,600)/(1+0.7623) \\ N(8)=(3600)/(1.7623) \\ N(8)=2042.79 \\ N(8)\approx2,043peoples \end{gathered}`

Hence the number of people infected after 8 days is approximately 2,043 peoples