Economists use Lorenz curves to illustrate the distribution of income in a country. A Lorenz curve, y = f (x), represents the actual income distribution in the country. In this model, x represents percents of families in the country from the poorest to the wealthiest and y represents percents of total income. The model y = x represents a country in which each family has the same income. The area between these two models, where 0 ≤ x ≤ 100, indicates a country’s “income inequality.” The table lists percents of income y for selected percents of families x in a country.

(a) Use a graphing utility to find a quadratic model for the Lorenz curve.(b) Plot the data and graph the model.(c) Graph the model y = x. How does this model compare with the model in part (a)?(d) Use the integration capabilities of a graphing utility to approximate the “income inequality.”

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10 y 3.35 X X y 60 28.03 30 6.07 9.17 13.39 20 70 39.77 80 55.28 40 50 19.45 90 75.12