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

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(20054) (Show Source): You can put this solution on YOUR website!

, or whatever letters your teacher/book uses.
A bacteria culture is started with 100 bacteria.
So A₀ = 100
After 7 hours, the population has grown to 600 bacteria.
A_f = 600 when t = 7
find the rate of growth in percent
About 25.6% Edwin

Answer by greenestamps(13200) (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:

= 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

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