Question

If you earned up to $113,700 in 2013 from an employer, your social security tax rate was 6.2% of your income. If

you earned over $113,700, you paid a fixed amount of $7,049.40.
a. Write a piecewise linear function to represent the 2013 social security taxes for incomes between $0 and
$500,000.

Answer 1

`f(x)=\left \{ {{0.062x ;0\leq x\leq 113,700} \atop {7049.40;113,700\leq x \leq500,000}} \right.` where f(x) is the the social security taxes in dollars and x is the amount earned in 2013

Explanation:

The problem states that for the first $113,700 you will pay a tax rate of 6.2% for your income. When taking 6.2% of an amount you can turn the percentage into a decimal number and multiply it by the total income which will be represented by the letter x:

0.062x

for an interval of

`0\leq x\leq 113,700`

this is the first part of the piecewise defined function. For the next part, the problem states tht the social security tax will be a fixed amoun of $7,049.40, so the second part of the piecewise defined function would be just:

7,049.40

for an interval of

`113,700\leq x \leq500,000`

according to the specifications of the problem.

So the whole piecewise defined function will be

`f(x)=\left \{ {{0.062x ; 0\leq x\leq 113,700 } \atop {7049.40 ; 113,700\leq x \leq500,000 }} \right.` where f(x) is the the social security taxes in dollars and x is the amount earned in 2013