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Uni calculus, question on bacteria growth.?
A bacteria culture starts with 900 bacteria and grows at a rate proportional to its size. After 5 hours, there are 5000 bacteria.
A. Find an expression for the number of bacteria after hours.
B. Find the number of bacteria after 6 hours.
C. Find the growth rate after 6 hours.
D. After how many hours will the population reach 30000?
1 Answer
- cidyahLv 78 years agoFavorite Answer
A)
P(t) = 900 e^kt
When t=5, P(t) = 5,000
5,000 = 900 e^5k
e^5k = 5,00/900
5k = ln(5,000/900)
k=ln(5,000/900) / 5
k = 0.34296
P(t) = 900 e^0.34296t
B)
Plug t=6 into P(t)
P(6) = 900 e^0.34296(6) =7045.57
P(6) = 7046
C)
7046 = 900 e^6k
e^6k = 7046/900
6k = ln(7046/900)
k = ln(7046/900) / 6 = 0.3430
D)
30,000 = 900 e^0.34296t
e^0.34296t = 30,000/900
0.34296t = ln( 30,000/900)
t = ln(30000/900) / 0.34296
t=10.22 hours
