So, how did you arrive at these answers? If we disagree, then there's something to check.
and on C, what are the "new" bacteria? Those which have grown during the last hour? The last minute? If you got B right, then C should then be easy to answer.
A culture of bacteria is growing at a rate of 4e^0.5t per hour, with t in hours and 0 ≤ t ≤ 20.
A) How many new bacteria will be in the culture after the first six hours? ( I got 153 bacteria)
B) How many new bacteria are introduced from the end of the fifth hour through the fifteenth hour? (I got 23687 bacteria)
C) At approximately how many hours after t=0 will the culture contain 200 new bacteria? (idk.)
please check my answers, and show your work. Thanks!
2 answers
(A) if you mean how many total bacteria have grown during the first 6 hours, then that is of course ∫[0,6] 4e^(t/2) dt = 8(e^3 - 1) = 152.684... round it is 153
which is right
(B) ∫[5,15] 4e^(t/2) dt = 14366.879...round to get 14367
(C) ∫[0,x] 4e^(t/2) dt = 200
8(e^(x/2) - 1) = 200
e^(x/2) - 1 = 25
e^(x/2) = 26
x/2 = ln26
x = 2 ln26 = 6.516
which is right
(B) ∫[5,15] 4e^(t/2) dt = 14366.879...round to get 14367
(C) ∫[0,x] 4e^(t/2) dt = 200
8(e^(x/2) - 1) = 200
e^(x/2) - 1 = 25
e^(x/2) = 26
x/2 = ln26
x = 2 ln26 = 6.516
2 answers