Question

11-A pathologist observes that the bacteria in the dish have been growing exponentially from 1000 to 1800 between 1 p.m. and 3 p.m. (8 pts.) a) Given that the growth is exponential, N = Noe't where N is the number of bacteria and No is the initial bacteria count, use the information to find r, rounded to 3 decimal places. Hint: 1 p.m. is when t = 0. b) How many bacteria (to the nearest whole number) should the pathologist expect at the time she leaves at 6 p.m.? c) At what time can she expect to have 4000 bacteria?

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Answer 1

Answer of bacteria after N = No ert since bacteria in the dish have been growing exponentially from 2000 to 1800 between 1pm to 3pm ie in a hours, N= Number time t (noun) No 7 dnitial bacteria at time t (houn ta time in hours growth rate. N = 1800, No 1000 to 2hrs, da? N = No est t=? 2 2 293 Na 4000 No: 1000 8x2 1800 - 1000 e 1800 e82 :. N= No ert .293xt uboo - 1000 e colo 2 882 6.2937 Applying 6 both sides In both sides Applying in a 9 Ine 82 (ne=' .58778666572 & Ln(4) = lne 293t 1.8862943 = -2434 5[ne34] .587786665 2. -6. 1.3862943 293 8: 293893333 [t = 4.313 ] ho [ 4hus 4Spain ] [x = 1293 I Ans) Non N=?, ta 6-1 = 5 hos all 1000 1 da 293 [After 4hrs 46 min the backsia N= No ert e 5x count in 4000 ] (401), 293 = 1000 x e 1.469 - 1000 xe 1ooo X 4.3448 = 4844.888 N 4345 (At 6pm the bacteria count is 4345 J Ans)