In 1978, the Social Security and Medicare rate combined was 6.05%, up to $17,700 earned. Express the Social Security tax s(x) for 1978 as a piecewise function. Ten years later, the percent had increased to 7.51% and the maximum taxable income had increased to $45,000. Express the Social Security tax s(x) for 1988 as a piecewise function. If a person earned $50,000 in 1978, and $50,000 in 1988, what was the difference in the Social Security and Medicare taxes paid?

Step-by-step explanation:

From the given question:

a) The piecewise function for the Social Security tax s(x) is expressed as:

s(x) = x * 6.05% when x < $17,700

The 6.05% of the given amount is:

= (6.05/100) * 17700

= 1070.85

s(x) = 1070.85 when x ≥ $17,700

b) Ten years later, i.e. 1988; the percentage had increased to 7.51% & maximum taxable income also increased to $45000

The piecewise function for the Social Security tax s(x) is expressed as:

s(x) = x * 7.51% when x < $45,000

The 7.51% of the given amount is:

= (7.51/100) * 45000

= 3379.5

s(x) = 3379.5  when x ≥ $45,500

c) The difference in the Social Security and Medicare taxes paid is as follows:

In 1978, s(x) = 1070.85 when x ≥ $17,700

In 1988, s(x) = 3379.5  when x ≥ $45,500

The difference in the Social Security and Medicare taxes paid  = $3379.5 - $1070.85

The difference in the Social Security and Medicare taxes paid = $2308.65

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step-by-step explanation:

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