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October 11th, 2013, 11:24 AM  #1 
Newbie Joined: Oct 2013 Posts: 10 Thanks: 0  Help on a algebra 2 word problem
The formula r = 2^(1/x)  1 gives the annual interest rate, r, required for your money to double in x years. If it takes 18 years for your money to double, what was the approximate annual interest rate? 
October 11th, 2013, 11:34 AM  #2 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,958 Thanks: 1146 Math Focus: Elementary mathematics and beyond  Re: Help on a algebra 2 word problem
r = 2^(1/1  1 ? 0.04

October 11th, 2013, 01:16 PM  #3 
Newbie Joined: Oct 2013 Posts: 10 Thanks: 0  Re: Help on a algebra 2 word problem
the thing is the answers are 2,4,8,18

October 11th, 2013, 02:58 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 20,919 Thanks: 2202 
Note that 0.04 is 4%.

October 11th, 2013, 04:09 PM  #5 
Newbie Joined: Oct 2013 Posts: 10 Thanks: 0  Re: Help on a algebra 2 word problem
How would you be able to get that answer without using a calculator? And thank you, I don't know how I missed that lmao. 
October 12th, 2013, 12:39 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 20,919 Thanks: 2202 
Divide 72 by 18 to get 4. This is roughly right and doesn't require a calculator if you can do division by 18 mentally. Note: 72 is chosen to make the arithmetic a bit easier. It would be a bit more accurate to use 71 (or 70 for larger divisors), but the calculation is not expected to be highly accurate anyway. This integer is approximately 100ln(2). The method remains approximate even if the exact value of 100ln(2) is used. 

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