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.

Question

Jan Wiley

Business

28 May, 06:10

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.

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Jonah Salinas · 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.