Question

In a town whose population is 2600, a disease creates an epidemic. The number of people N infected t days after the disease has begun is given by the function N(t)- 2600 1+34 -0.6t. Complete parts a) through c) below a) How many are initially infected with the disease (t = 0)? (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 . (Round to the nearest whole number as needed.) The number infected after 5 days is . (Round to the nearest whole numbers as needed.) The number infected after 8 days is (Round to the nearest whole numbers as needed.) The number infected after 12 days is . (Round to the nearest whole numbers as needed.) The number infected after 16 days is . (Round to the nearest whole numbers as needed.) c) Using this model, can you say whether all 2600 people will ever be infected? Explain. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. Ast+e, N()+2600, so 2600 people will be infected after days. OB. Ast-O, N(t)-2600, so 2600 people will be infected after days. O c. Asto, N(t)-2600, so the number approaches 2600, but never actually reaches it

Answer 1

N(t) = 2.607. Teoret 2600 142 -0.6t .le a) initially infected as to NO - 2600 - 2600 2600 23.) 1+22.1 (+22.1 2600 339.58340 = 112.554 - 113 - No of initially infected people =113 | b) N (2) = 2600 1+ 22.120.6) Number infected after 2 days is 3401 N(5) = 2600 acre) = 1237.9221238 [Number infected after 5 days = 1238 | N(8) = 2600 2 2200 1+22.120.6x8 = 2199.892 Number infected after 8 days = 2200 l N (2) = 2600 H+ 2210-6812 -2357 +975 = 2558 Number infected after 12 days = 2558 N(16) = 2600 = 2599.823 ~ 2600 1722-1 € 0.6x16 Number infected after 16 days 2600 I nearly 2600 --- 1+ 22-1 2600 ttt N2) = 2600 1+22.1.-0.6 x c) As t-2 N(+) 2600, so the number approaches 2600, but never actually reaches ik. . is correct. O