SOLUTION: A bacteria culture is started with 100 bacteria. After 7 hours, the population has grown to 600 bacteria. If the population grows exponentially, find the rate of growth in percent

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Question 1205144: A bacteria culture is started with 100 bacteria. After 7 hours, the population has grown to 600 bacteria. If the population grows exponentially, find the rate of growth in percent
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

A%5Bf%5D=A%5B0%5De%5E%28rt%29, or whatever letters your teacher/book uses.
A bacteria culture is started with 100 bacteria.
So A0 = 100
A%5Bf%5D=100e%5E%28rt%29
After 7 hours, the population has grown to 600 bacteria.
Af = 600 when t = 7

600=100e%5E%28r%2A%287%29%29

6=e%5E%287r%29

ln%286%29=7r

ln%286%29%2F7=r

0.2559656385=r
find the rate of growth in percent
About 25.6%

Edwin

Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


Since the problem doesn't specify, I will assume that the percent growth PER HOUR is what the problem is asking for.

In 7 hours the population increases by a factor of 600/100 = 6:

%281%2Bx%29%5E7=6
1%2Bx=6%5E%281%2F7%29 = 1.2917 to 4 decimal places

x = 1.2917-1 = 0.2917

ANSWER: growth rate per hour = 0.2917, or 29.17%

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NOTE: My solution and Edwin's solution are equivalent -- using different definitions of "growth rate":

e^0.2559656385 = 1.291708342