For a family with an income in the lowest fifth of the U.S. population, the mean household income for the years 2000 to 2018 can be approximated (in thousands of dollars) by ƒ(t) = 0.00354t³ - 0.0762t² + 0.608t + 13.71, where t is the number of years since 2000. The mean household for a family in the top 5% can be approximated by g(t) = 0.0465t³ - 0.888t² + 11.3t + 278.

(a) Find the area under ƒ(t) over the interval 0 ≤ t ≤ 18. Interpret your results.
(b) Find the area under g(t) over the interval 0 ≤ t ≤ 18. Interpret your results.
(c) Find the area between the two curves over the interval 0 ≤ t ≤ 18. Interpret your results.
(d) Discuss what your results tell us about income inequality.