Question

This exercise uses the population growth model. The count in a culture of bacteria was 400 after 2 hours and 25,600 after 6 hours. (a) What is the relative rate of growth of the bacteria population? Express your answer as a percentage. (Round your answer to the nearest whole number.) 104 % (b) What was the initial size of the culture? (Round your answer to the nearest whole number.) 200 x bacteria (c) Find a function that models the number of bacteria n(t) after t hours. (Enter your answer in the form noert Round your no value to the nearest whole number. Round your r value to two decimal places.) n(t) = (d) Find the number of bacteria after 4.5 hours. (Round your answer to the nearest hundred.) bacteria (e) After how many hours will the number of bacteria reach 50,000? (Round your answer to two decimal places.)

Answer 1

A count 25,6oot ť (time) fount CCT) = noert - (r= t= Yis - ii) rate time of growth (Ca)=400 = no per C(6)= 25,600 = no rear 400 Divide (l) by a 25.600 = 96 eft S toer 64= 48 - Apply . In on both side. In 64 = ln. eur - dorot en 2o = ler line - [colmabablna? 6 ln (2)=42 lone roolne=17 psGln(2) 21.0397 4 r ã 1004 →in fraction ie 104% > in percent. __ las 11044 . Ane I by Initial singe of culture her ulture = clog

(12) = 400 = no el 04x2 lno a 400 2008 Inoz 4909720 scal = no exo = no eo [eo=17 ecoy = no = 4909720 Ino A501 Ang. Isolang. (bacteria) nit) = 49.9720 e out - n(t) = 50 el044 Ang. (af tey rounding) C(405) = 250 x 10707700 50. eloy x 905 5,38805 û 15400 . CCt) = 50,000 t =? elo04t. - 50,000 elrout = 1000 Apply in both C sides , Tolne=1] line out = ln 103 1004t line = 3 los 10 - t = 3 dno) lolle t=6.8420 t = 16.64 hr. com
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