Question

From 1960 rough 1995 payments in millions of dollars for Medicaid can be modeled by the polynomial 411x^2 + 156x + 24050, where x = 0 corresponds to 1980. Approximate the amount of payments for the years 1982, 1981, 1984, and 1985. In the year 1982, the payments were approximately?

A) 15.27 million
B) 14.85 million
C) 15.14 million
D) 14.73 million.

Answer 1

The polynomial 411x^2 + 156x + 24050 models Medicaid payments in millions of dollars since 1980. For the year 1982 (x=2), the approximation is $26,006 million, which aligns with none of the provided answer choices as they are not in the correct scale.

Step-by-step explanation:

The polynomial given, 411x^2 + 156x + 24050, models Medicaid payments in millions of dollars, where x is the number of years since 1980. To find the Medicaid payments for the years 1982, 1981, 1984, and 1985, we must substitute x with the appropriate values (2, 1, 4, and 5, respectively).

For 1982 (x = 2):
P(2) = 411(2)^2 + 156(2) + 24050
P(2) = 411(4) + 312 + 24050
P(2) = 1644 + 312 + 24050
P(2) = 26006 million dollars

Following this method for the other years gives us:

• 1981 (x = 1): P(1)
• 1984 (x = 4): P(4)
• 1985 (x = 5): P(5)

The approximate payment for Medicaid in the year 1982, to the nearest hundredth million dollars, is $26,006 million (Option A, $15.27 million, does not fit within the calculation).