Afirm decides to increase output at a constant relative rate from its current level of 20,000 to 30,000 units during the next five years. calculate the annual percent rate of increase required to achieve this growth.

8.45%  
Here's we're looking for a geometric increase from 20,000 to 30,000 over a period of 5 years. So the equation is
 20000*X*X*X*X*X = 30000
 20000*X^5 = 30000
 X^5 = 30000/20000
 X^5 = 1.5 
 So we need the 5th root of 1.5. We can do that using logarithms.
 10^(log(1.5)/5)
 = 10^(0.176091259/5)
 = 10^0.035218252
 = 1.084471771 
 So 1.084471771^5 = 1.5
 Since we're looking at the percentage increase and 1 = 100%, we can just subtract the 1 and get 0.084471771 which is 8.4471771% or a 8.45% annual growth rate.

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