SOLUTION: The number of bacteria present in a culture after t minutes is given as B= 100e^kt. IF there are 5287 bacteria present after 13 minutes, find k.

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Question 60480: The number of bacteria present in a culture after t minutes is given as
B= 100e^kt. IF there are 5287 bacteria present after 13 minutes, find k.
Answer by smik(40) About Me  (Show Source):
You can put this solution on YOUR website!
Good question. Great question. Let's go through it.


So, we start of with the equation B=100e^kt, and the fact that B=5287 when t=13. With this in mind we can easily solve for k as shown below:


5287+=+100e%5E%2813k%29 (divide both sides by 100)
52.87+=+e%5E%2813k%29 (natural log of both sides, which cancels out the e)
ln%2852.87%29+=+13k (divide both sides by 13)
ln%2852.87%29%2F13+=+k
k+=+0.305 (to three significant figures)


Hope all that helps.