VOTING PATTERN After a presidential election, the proportion h(p) of seats in the House of...

VOTING PATTERN After a presidential election, the proportion h(p) of seats in the House of Representatives won by the party of the winning presidential candidate may be modeled by the “cube rule”

where p is the proportion of the popular vote received by the winning presidential candidate.

a. h'(p) and h"(p).

b. Sketch the graph of h(p).

c. In 1964, the Democrat Lyndon Johnson received 61% of the popular vote. What percentage of seats in the House does the cube rule predict should have gone to Democrats? (They actually won 72%.)

d. For the most part, the cube rule has been extremely accurate for presidential elections since 1900. Use the Internet to research the actual proportions that occurred during these elections and write a paragraph on your findings.