Question

the count in a bacteria culture was 400 after 10 minutes and 1300 after 30 minutes. assuming the count grows exponentially, what was the initial size of the culture? find the doubling period. find the population after 95 minutes. when will the population reach 15000.

1. thienthanh
Assuming the Bacteria count grows the exponential initial size of the culture is 400.
At t = 0, the initial population size is given by:
P(0) = 400
The doubling period can be found using the following formula:
T = ln2/r
Where r is the exponential growth rate.
Using the data from the question, we can calculate the exponential growth rate:
r = [ln(1300) – ln(400)]/(30 – 10) = 0.12
The doubling period is then given by:
T = ln2/r = 5.7 minutes
The population at t = 95 minutes can be calculated using the equation:
P(95) = P(0) * (2^(r*95))
P(95) = 400 * (2^(0.12*95)) = 7114
The time taken to reach a population of 15000 can be found using the equation:
t = (ln(15000/P(0))/r
t = (ln(15000/400))/0.12 = 97.2 minutes
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