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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)

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 Pi class=

Respuesta :

Answer:

2,043 peoples

Explanations:

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

[tex]N(t)=\frac{3600}{1+18.7e^{-0.4t}}[/tex]

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;

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

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

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