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 below. (Note: t=0 represents 1970.)
t 0 1 2 3 4
P(t) 203 227 248 281 309
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 in millions of people per decade from 1970 to 2000, we need to calculate the total change in population from 1970 to 2000 and then divide by the total number of decades.
From the table, we can see that:
- P(0) = 203 million
- P(3) = 281 million
The total change in population from 1970 to 2000 is:
281 million - 203 million = 78 million
The total number of decades from 1970 to 2000 is:
2000 - 1970 = 30 years = 3 decades
Now, we can find the average rate of change in millions of people per decade:
Average rate of change = Total change in population / Total number of decades
Average rate of change = 78 million / 3 decades
Average rate of change ā 26 million per decade
Therefore, the average rate of change in millions of people per decade in the U.S. population from 1970 to 2000 is approximately 26 million.