Question

In a town whose population is , a disease creates an epidemic. The number of people N infected t days after the disease has begun is given by the function . Complete parts a) through c) below.a) How many are initially infected with the disease ?nothing (Round to the nearest whole number as needed.) b) Find the number infected after 2 days, 5 days, 8 days, 12 days, and 16 days.The number infected after 2 days is nothing. (Round to the nearest whole number as needed.) The number infected after 5 days is nothing. (Round to the nearest whole numbers as needed.) The number infected after 8 days is nothing. (Round to the nearest whole numbers as needed.) The number infected after 12 days is nothing. (Round to the nearest whole numbers as needed.) The number infected after 16 days is nothing. (Round to the nearest whole numbers as needed.) c) Using this model, can you say whether all people will ever be infected? Explain. Select the correct choice below and, if necessary, fill in the answer box to complete your choice.A.As t0, N(t), so people will be infected after nothing days.B.As te, N(t), so people will be infected after nothing days.C.As t, N(t), so the number approaches , but never actually reaches it.

Answer 1

a) How many are initially infected with the disease ​(t = 0)? 211 people.

`\begin{gathered} N(t)=(4500)/(1+20.3e^(-0.4t)) \\ N(0)=(4500)/(1+20.3e^(-0.4(0))) \\ N(0)=(4500)/(1+20.3)_{} \\ N(0_{})\approx211 \end{gathered}`

b. The number infected after 2 days 445 people.

`\begin{gathered} N(t)=(4500)/(1+20.3e^(-0.4t)) \\ N(2)=(4500)/(1+20.3e^(-0.4(2))) \\ N(2)=(4500)/(10.12137797) \\ N(2)\approx445 \end{gathered}`

c. The number infected after 5 days is 1,201 people.

`\begin{gathered} N(5)=(4500)/(1+20.3e^(-0.4(5))) \\ N(5)=(4500)/(3.74730625) \\ N(5)\approx1201 \end{gathered}`

d. The number infected after 8 days is 2,462 people.

e. The number infected after 12 days 3,856 people.

f. The number infected after 16 days 4,353 people.

All 4500 people will be infected after 31 days.