Question

The count in a bateria culture was 100 after 10 minutes and 2000 after 40 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 13000

Answer 1

let A be the bacteria population after t minutes, A0 be the initial bacteria population.

using equation\[A = A _{0} e^{kt}\]

solve for A0 and k simultaneously. \[k = \frac{ \ln 20 }{ 30 } = 0.09986\] and \[A _{0} \approx 37\] (actual answer would be 36.8 )

to find the doubling time, \[\frac{ A }{ A _{0} } = 2 = e ^{kt}\]
solving for t, t = 70.2989 minutes.
JUST SUBSTITUTE VALUES TO THE INITIAL EQUATION TO SOLVE FOR OTHER PROBLEMS. =)

Answer 2

thanks!