Dependency ratio the share of the world population that is

Question

Question: Dependency ratio the share of the world population that is over 60 years of age compared to the rest of the working population in the world is of concern to economists. An increasing dependency ratio means that there will be fewer workers to support an aging population. The dependency ratio over the next century is forecast to be

R(t) = 0.00731t⁴ - 0.174t³ + 1.528t² + 0.48t + 19.3          (0 ≤ t ≤ 10)

In year t, where t is measured in decades with t = 0 corresponding to 2000.

A. Show that the dependency ratio will be increasing at the fastest pace around 2052. Hint: use the quadratic formula.

B. What will the dependency ratio be at that time?