SOLUTION: A population of bacteria grows according to A=5000e^(.025t) how long will it take for the population to double? Thank you

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Question 387316: A population of bacteria grows according to A=5000e^(.025t) how long will it take for the population to double?
Thank you
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
The time the population takes to double remains the same no matter where we pick t. Given this, set t = 0. Then A = 5000e^0 = 5000. Now, set A = 10000 so that we can find t:

10000+=+5000e%5E%28.025t%29

2+=+e%5E%28.025t%29

ln+2+=+.025t

t+=+40+ln+2 = 27.73 (whatever the units of time are)