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
t,0,1,2,3,4
p(t) 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.
To find the average rate of change from 1970 to 2000, we need to calculate the change in population from t=0 to t=3, and then divide by the time passed:
Change in population = p(3) - p(0) = 281 - 203 = 78 million
Time passed = 3 decades
Average rate of change = Change in population / Time passed
Average rate of change = 78 million / 3 decades = 26 million per decade
Rounded to the nearest whole number, the average rate of change in the U.S. population from 1970 to 2000 is 26 million people per decade.