Find the average rate of change in the country's population between 1990 and 2010.

Question

The population of a certain country since 1990 can be approximated by f(t) = 0.008t² + 2.1t + 175 where f (t) is the population in millions and t represents the number of years since 1990. Find the average rate of change in the country's population between 1990 and 2010. Round to 1 decimal place.

Answer 1

As t represents the number of years since 1990, the population for 1990 is obtained by putting zero in the equation yielding 175 million. Twenty year later (t=20), the population calculated is 220.2 million. The average rate of change is obtained by subtracting 175 from 220.0 and dividing by 20 to give the population change per year. The result rounded to one decimal place is 2.3 million/year.