SOLUTION: I need your help on the following word problem: Given a starting population of 100 bacteria, the formula b=100(2^t) can be used to find the number of bacteria, "b", after "t" peri

Question 190620: I need your help on the following word problem:
Given a starting population of 100 bacteria, the formula b=100(2^t) can be used to find the number of bacteria, "b", after "t" periods of time. If each period is 15 minutes long, how many minutes will it take for the population of bacteria to reach 51,200?
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Plug in (the given bacteria population)

Divide both sides by 100.

Take the log base 10 of both sides

Rewrite right side using the identity

Divide both sides by

Use the change of base formula to rewrite the left side

Note: Remember the change of base formula is

Rearrange the equation

Evaluate the log base 2 of 512 to get 9

Note:

since , this means that

So the answer is which means that it will take 9 minutes for the population to reach 51,200
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