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Interpreting Average Rates of Change with Real-World Examples

4.8.5 Interpreting Average Rates of Change with Real-World Examples

4.8.5 • Interpreting Average Rates of Change with Real-World Examples

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Line graph showing population in thousands from 1900 to 2000. Population rises from about 20,000 in 1900 to a peak near 45,000 around 1950, then declines to around 25,000 by 2000.

The graph above shows the population of a city from 1900 to 2000. Use the graph to answer questions 1 – 5.

1.

What is the average rate of change of the population between 1930 and 1950? Be prepared to show your reasoning.

Compare your answers:

About 250 people per year. The population was 40,000 in 1930 and about 45,000 in 1950, an increase of 5,000 people over 20 years, which equals 250 people per year.

2.

Decide if the average rate of change is positive or negative for the time period from 1930 to 1940.

positive.

3.

Decide if the average rate of change is positive or negative for the time period from 1950 to 1970.

negative.

4.

Decide if the average rate of change is positive or negative for the time period from 1930 to 1970.

negative.

5.

In which decade (10-year interval) did the population grow the fastest? Explain how you know.

Compare your answers:

From 1910 to 1920. For example: The graph has the steepest slope between the two points on the graph (1910,22)(1910,22) and (1920,32)(1920,32).