# Math/Pre-calculus

Assume that the number of bacteria follows an exponential growth model:
P(t)=P0e^k/t. The count in the bacteria culture was 400 after 10 minutes and 1500 after 35 minutes.
(a) What was the initial size of the culture?
(b) Find the population after 85 minutes.
(c) How many minutes after the start of the experiment will the population reach 12000?

1. P = Po e^kt
400 = Po e^10k
1500 = Po e^35 t

1/Po = (1/400) e^10 k = (1/1500)e^35 k

e^35 k / e^10k = 1500/400 = 15/4

e^25 k = 15/4

25 k = ln(15/4) = 1.322

k = .0529
so

P = Po e^.0529 t
400 = Po e^.529
Po = 236
then
P = 236 e^.0529 t

I think you can take it from there

posted by Damon
2. I think you have a typo or a flaw in your equation.

P(t) = P0 e^(k/t) makes no sense at t = 0
and since you are asking for the initial value P0, that would assume we need t = 0 in our calculation.
That would make our result undefined.

posted by Reiny
3. Did not see Damon's answer, I had the page open all this time.

posted by Reiny

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