# Math/Pre-calculus

posted by liza

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. Damon

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

2. Reiny

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.

3. Reiny

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

## Similar Questions

1. ### precalculus

A bacteria culture initially contains 1500 bacteria and doubles every half hour. a) Find an expression for the number of bacteria after t hours. Q(t)= b) The number of bacteria after 20 minutes is (the answer must be an integer) c) …
2. ### pre calculus

if there are initial 2500 bacteria in a culture, and the number of bacteria double each hour, the number of bacteria after t hours cab n be found using the formula=N=2500(2^t).how long will it take the culture to grow to 75,000 bacteria.
3. ### Calc

The number of bacteria in a culture is increasing according to the law of exponential growth. There are 125 bacteria in the culture after 2 hours and 350 bacteria after 4 hours. a) Find the initial population. b) Write an exponential …
4. ### MATH :)

3. In Biology, it is found that the bacteria in a certain culture double every half-hour. If the initial number of bacteria in culture is 1000, A. Find the defining equation for the number N of bacteria in culture after T hours, assuming …
5. ### calculus

2. The rate of change in the number of bacteria in a culture is proportional to the number present. In a certain laboratory experiment, a culture has 10,000 bacterial initially, 20,000 bacteria at time t1 minutes, and 100,000 bacteria …
6. ### calculus

The count in a bacteria culture was 600 after 10 minutes and 1100 after 30 minutes. What was the initial size of the culture?
7. ### College Algebra

The number of bacteria in a certain culture increased from 500 to 1000 between 7:00 A.M. and 9:00 A.M. Assuming growth is exponential, the number f(t) of bacteria t hours after 7:00 A.M. is given by f(t) = 500(2)^t/2. (a) Estimate …
8. ### Calculus (math)

A bacteria culture grows with constant relative growth rate. The bacteria count was 784 after 2 hours and 117649 after 6 hours. What is the relative growth rate?