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 of the values for this function are shown in the table. (Note: t=0 represents 1970) What was the average rate of change, in millions of people per decade, in the US population from 1970 to 2000? Round to the nearest whole number
This is the table shown,
t 0, 1, 2, 3, 4
P(t) 203, 227, 249, 281, 309
To find the average rate of change in the US population 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.
Step 1: Find the population in 1970 (t=0) and 2000 (t=3)
Population in 1970 (t=0): P(0) = 203
Population in 2000 (t=3): P(3) = 281
Step 2: Calculate the total change in population from 1970 to 2000
Total change = P(3) - P(0) = 281 - 203 = 78 million
Step 3: Calculate the total number of decades from 1970 to 2000
Total decades = 2000 - 1970 = 30 years = 3 decades
Step 4: Calculate the average rate of change in millions of people per decade
Average rate of change = Total change / Total decades
Average rate of change = 78 / 3 ≈ 26 million people per decade
Therefore, the average rate of change in the US population from 1970 to 2000 was approximately 26 million people per decade.