[table]
Alesha found data showing Canada's population in each year from 1975 to 2005. Determine the average rate of change in Canada's population for the interval from 1980 to 2000. (up to three decimal places) Source: Statistics Canada Catalogue no: 98-187XIE (www.statcan.ca/english/freepub/98-187-XIE/pop.htm) |
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Question

BlackTom AI · Accepted Answer

The question asks for the average rate of change in Canada's population from 1980 to 2000 using the provided table.

First, identify the populations for the endpoints:
- 1980: 24,516,071
- 2000: 30,689,035

Next, compute the total change in population over the interval: 30,689,035 − 24,516,071 = 6,172,964.

Then determine the length of the interval in years: 2000 − 1980 = 20 years.

Finally, divide the total change by the number of years to obtain the average rate of change per year: 6,172,964 ÷ 20 = 308,648.2.

Expressed to three decimal places, the average rate of change is 308648.200.

Notes on potential confusion: if one mistakenly uses 21 years (by counting endpoints inclusively) or misreads the endpoint populations, the result will differ. The standard approach for average rate of change over a closed interval [a, b] is to subtract the initial value at a from the final value at b and divide by (b − a).

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