MATH SOLVE

10 months ago

Q:
# From 2017 to 2020, registration at a dance school underwent three annual increases of 16%, 15% then 20%. calculate the average annual rate of change, to the nearest 0.01%

Accepted Solution

A:

To calculate the average annual rate of change over the three years, we need to find the geometric mean of the individual annual growth rates.
For the first year (2017 to 2018), the increase is 16%.
For the second year (2018 to 2019), the increase is 15%.
For the third year (2019 to 2020), the increase is 20%.
To find the average annual rate of change, calculate the geometric mean as follows:
Average rate of change = [(1 + growth rate1) * (1 + growth rate2) * (1 + growth rate3)]^(1/3) - 1
Convert the percentages to decimal form:
Growth rate for the first year: 16% = 0.16
Growth rate for the second year: 15% = 0.15
Growth rate for the third year: 20% = 0.20
Calculate the average annual rate of change:
Average rate of change = [(1 + 0.16) * (1 + 0.15) * (1 + 0.20)]^(1/3) - 1
Average rate of change ≈0.1698
To the nearest 0.01%, the average annual rate of change in registration at the dance school over the three years is approximately 16.98%.