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10.Medicare Premiums. The monthly Medicare Part B health-care premium for most e

ID: 3137336 • Letter: 1

Question

10.Medicare Premiums. The monthly Medicare Part B health-care premium for most eficiaries ages 65 and older has increased significantly since 1975. The monthly premium has increased from about $7 in 1975 to $110.50 in 2011 (Source: Centers for Medicare and Medicaid Services). The following exponential function models the premium increases: M(x) 7(1.080)* where x is the number of years since 1975. Estimate the monthly Medicare Part B premium in 1985, in 1992, and in 2002. Round to the nearest dollar. 11T)Charitable Giving. Over the last four decades, charitable giving in the United States has grown exponentially from approximately $20.7 billion in 1969 to approximately $303.8 billion in 2009 (Sources: Giving USA Foundation: Volunteering in America by the Corporation for National&Community; Service). The function G(x)-20.7(1.06946)* where x is the number of years since 1969, can be used to estimate charitable giving, in billions of dollars. Find the amount of charitable giving in 1978, in 1985, and in 2000.

Explanation / Answer

M = 7(1.080)x

For 1985, x = 10

M = 7(1.080)10

= 15.112

Premium in 1985 = $15.112

For 1992, x = 17

M = 7(1.080)17

= 25.9

Premium in 1992 = $25.9

For 2002, x = 27

M = 7(1.080)27

= 55.91

Premium in 2002 = $55.91

G = 20.7(1.06946)x

For 1978, x = 9

G = 20.7(1.06946)9

= $37.883 billion

For 1985, x = 16

G = 20.7(1.06946)16

= $60.618 billion

For 2000, x = 31

G = 20.7(1.06946)31

= $165.985 billion