Question

The population of Town A in 1980 was 3000.

The population of Town A increased by 20% every decade. Let x represent the number of decades since 1980. The graph shows the population of Town B.
Compare the populations of the towns by calculating and interpreting the average rates of change from 2000 to 2020.

Answer 1

Explanation:

The population of Town A in 2000 was 3000(1.2)^2 = 5184. The population of Town A in 2020 was 3000(1.2)^4 = 8947.2. The average rate of change of Town A from 2000 to 2020 is (8947.2-5184)/(2020-2000) = 188.64 people per year.

From the graph, the population of Town B in 2000 was approximately 5500. The population of Town B in 2020 was approximately 7000. The average rate of change of Town B from 2000 to 2020 is (7000-5500)/(2020-2000) = 75 people per year.

Therefore, the average rate of change of Town A's population is greater than that of Town B's population from 2000 to 2020.