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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Business

Lisa

20 January, 14:23

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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Walker Weiss · 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.