SOLUTION: The count in a bacteria culture was 400 after 10 min and 1500 after 35 min what was the initial size of the culture? find doubbling period? find population after 90 min? when wi

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Question 458292: The count in a bacteria culture was 400 after 10 min and 1500 after 35 min what was the initial size of the culture?
find doubbling period?
find population after 90 min?
when will the population reach 12000?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
After some cumbersome algebra, the formula for the exponential growth is given by
B%28t%29+=+400%2A%2815%2F4%29%5E%28%28t-10%29%2F25%29.
The initial number is given by B(0) = 400%2F%2815%2F4%29%5E0.4
To find the doubling period,
==> 2+=+%2815%2F4%29%5E%28%28t-10%29%2F25%29
==> ln2+=+%28%28t-10%29%2F25%29%2Aln%2815%2F4%29
==> %2825+ln2%29%2Fln%2815%2F4%29+=+t-+10
==> %2825+ln2%29%2Fln%2815%2F4%29+%2B+10=+t
==> t = 23.11 minutes, approximately.