SOLUTION: How do i work out a problem when given How long will it take for the population of a certain country to double if its annual growth rate is 5 percent? First I plugged in 5

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Question 137588: How do i work out a problem when given
How long will it take for the population of a certain country to double
if its annual growth rate is 5 percent?
First I plugged in 5 (for 5%) Log in my calculatorand the answer was 0.l698970004.
Do i move the decimal over 2 places to give me 16.989 years or
rather that it would take 17 years for the population to double.
I have researched everthing and am unable to come up with any samples on how to work out any problems given just the percent without a population number? Can you please help me understand how to do this?
Is it just a calculator problem?
Any help would be greatly appreciated.
Thank You.
Answer by Fombitz(13823) About Me  (Show Source):
You can put this solution on YOUR website!
The problem is in your base.
You are not using base 10.
Here's the equation that describes your problem.
N%28t%29=N%5B0%5D%281.05%29%5Et
At time t=0, your population is N%5B0%5D.
You're looking for t when N%28t%29=2%2AN%5B0%5D
2%2AN%5B0%5D=N%5B0%5D%281.05%29%5Et
2=%281.05%29%5Et
The base for your logarithm is 1.05.
log%281.05%2C2%29=t
You can transform that into a base 10 problem with a substitution.
t=log%2810%2C2%29%2Flog%2810%2C1.05%29
t=0.30103%2F.021189%29
t=14.2067%29
The time to double is 14.2067 years.
Checking the answer, you get:
N%28t%29=2N%5B0%5D