Question

A firm 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.

Answer 1

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.