Question

The number of U.S. citizens 65 and older from 1990 through 2050 is estimated to be growing at the rate of, R(t)=0.063t^2 -0.48t+3.87, (0 less than or = t less than or = 15) million people/decade, where t is measured in decades and t = 0 corresponds to 1900. Show that the average rate of growth of U.S. citizens 65 and older between 2000 and 2050 will be growing at almost twice the rate of that between 1950 and 2000.

Answer 1

The average rate of change between years a and b is

(R(b)-R(a))/(b-a)

Here, both intervals are 50 years, so things are convenient. You want to show that

R(150)-R(100) ≈ 2(R(100)-R(50))

So, just plug in your numbers and see what you get.

Answer 2

how did you get the 150? I was thinking it would be 50

Answer 3

since it's measured in decades

Answer 4

so it would not be 50 either but 5?

Answer 5

Oops. You are correct. So, make the fix and rerun the math.