Medicare Trust Fund Balance The year 1994 marked the 30th anniversary of Medicare. A 1994 pamphlet by Representative Lindsey O. Graham gave projections for the Medicare Trust Fund balance, shown in the table below.
a. Representative Graham stated, “The fact of the matter is that Medicare is going broke.” Use the data in the table to find when he predicted that this would happen.
b. Find a quadratic model to fit the data, with x equal to the number of years after 1990. When did this model predict that the Medicare Trust Fund balance would be 0?
c. The pamphlet reported the Medicare trustees as saying “the present financing schedule for the hospital insurance program is sufficient to ensure the payment of benefits only over the next 7 years.” Does the function in part (b) confirm or refute the value 7 in this statement?
d. Find and interpret the vertex of the quadratic function in part (b).
Year | Medicare Trust Fund Balance (billions of $) | Year | Medicare Trust Fund Balance (billions of $) |
1993 | 128 | 1999 | 98 |
1994 | 133 | 2000 | 72 |
1995 | 136 | 2001 | 37 |
1996 | 135 | 2002 | −7 |
1997 | 129 | 2003 | −61 |
1998 | 117 | 2004 | −126 |
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