Rule of 70 Assumptions & Calculations
Assumptions:
Rate of growth is in a percent %
(when given a decimal, multiply by 100 to get percent)
Common errors when converting decimal to % through multiplication by 100
Problem: Population growing at .002, how long will it take population to double?
Example 1: Take decimal number and when multiplying by 100 to get percent, you move
decimal place over too many times or in Example 2: you don’t convert decimal to percent.
Example 3: Correct Calculation.
Example 1: if rate of growth is .002 and move decimal place over 3 places instead of 2 when
multiplying by 100, the doubling time calculation to be off by a factor of 10.
70/2 = 35 years
Example 2: if rate of growth is .002 and you don’t multiply by 100 to get your percent, the
doubling time calculation will be off by a factor of 100.
70/.002 = 3500 years
Example 3: Correct Calculation:
.002x100 = .2%
 70/.2 = 350 years
Various methods to Calculate for Rule of 70
*Use ONE method that works best for you, don’t need to know all 3 methods*
70 = the doubling time for a quantity undergoing exponential growth (i.e. increasing by 100%)
r = growth rate for quantity
1. 70 / % r
70 /1.5% = 46.6 years
2. 700/ %x10
700/ r(10) If growth rate is in a decimal percentage than times both sides by 10
70 x 10 and Decimal % x 10 = 700 / r
Example 70/1.5%
70x10 = 700 1.5x10 = 15 700/15 = 46.6 years
3. Using decimals if growth rate is in decimal form
.7/ r/100 Convert 70 to .7/ and divide r by 100.
Example 70/1.5% or .7/.015 = 46.6 years