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# Exponential growth rate

A country's population doubled in 45 years. What is the exponential growth rate?Growth

### 1 Answer by Expert Tutors

Jonathan F. | Instructor of Finance, Accounting, Economics and StatisticsInstructor of Finance, Accounting, Econo...
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~ 1.6% ... using the law of 72 ( 72/45 = 1.6) which approximates the time or percentage growth it takes for a quantity to double or decay.

Using mathematical calculation y = a(1+b)^x, x is the number of years it has occured, a the original population, b the growth rate, y the population at the end of the term. (Financially speaking this is the same as a compounded growth rate in a bank account. Suppose we double a into y ( a =1 , y =2 , x = 45), and assume an annual compounding:

2 = 1(1+b)^45 ... we can solve for the b, ((2/1)^(1/45))-1 = b , which equals 0.015522, or 1.5522%

As you see we are close to our approximation :D

If this is assumed to be continuous growth as I see the logorithm tag there... approach it this way,

2= 1(e^r*45)... r = ln (2/1)/45 = 0.015403 ~ 1.5403%... pretty close to the other method --the difference is a result of the number of compounding periods. D: