The count in a bacteria culture was 200 after 15 minutes and 1600 after 30 minut

nitraiddQ

nitraiddQ

Answered question

2021-09-12

The count in a bacteria culture was 200 after 15 minutes and 1600 after 30 minutes. Assuming the count grows exponentially, what was the initial size of the culture? What was the doubling period?

Answer & Explanation

faldduE

faldduE

Skilled2021-09-13Added 109 answers

Formula for the exponential growth is given by:
A=A0ekt
Where,
A0= Initial size
k= Rate of increase
t= Time
Therefore,
For A=200 and t=15,
200=A0e15k
For A=1600 and t=30,
1600=A0e30k
Divide equation (2) by (1):
1600200=A0e30ka0e15k
8=e30k15k
e15k=8
15k=ln8
k=ln815
k=ln815
=0.1386
Plug the values in equation to find initial size:
200=A0e15(0.1386)
A0e2.079=200
=25.011
25
To find doubling period:
A0=25
k=0.1386
A=50
t= Doubling period
Therefore,
50=25e(0.1386)t
5025=e0.1386t
0.1386t=ln2
t=ln20.1386
=5.001
5 min

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?