The population of the United States from 1970 to 2010 can be modeled by a function where
��
is the population (in millions) and
�
is the time in decades since 1970. Some values for this function are shown in the table. (Note:
�=0
represents 1970.)
�
0
1
2
3
4
�(�)
203
227
249
281
309
What was the average rate of change, in millions of people per decade, in the U.S. population from 1970 to 2000? Round to the nearest whole number.
Your answer:
To find the average rate of change, we need to calculate the change in population from 1970 to 2000 and then divide by the number of decades.
Population in 1970 (�=0): 203 million
Population in 2000 (�=3): 281 million
Change in population: 281 - 203 = 78 million
Number of decades: 2000 - 1970 = 30 years, which is equivalent to 3 decades
Average rate of change: 78 million / 3 decades = 26 million per decade
Therefore, the average rate of change in the U.S. population from 1970 to 2000 was 26 million per decade.