The population of the United States from 1970 to 2010 can be modeled by a function where P (t) is the population (in millions) and t is the time in decades since 1970. Some values for this function are shown in the table. (Note: t 0 represents 1970.)
t
P(t)
0
1
203
227
2
249
3
281
4
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.
To find the average rate of change from 1970 to 2000, we need to calculate the change in population over that time period and then divide by the number of decades.
The population in 1970 (t=0) was 203 million, and in 2000 (t=3) it was 281 million.
Change in population = 281 - 203 = 78
Number of decades = 3
Average rate of change = Change in population / Number of decades
Average rate of change = 78 / 3
Average rate of change ā 26
Therefore, the average rate of change in the U.S. population from 1970 to 2000 was approximately 26 million people per decade.