Question

The fictitious state of Aribraska has a graduated state income tax.

Residents pay 3% on the first $15,000 of income.
The next $25,000 earned is taxed at a rate of 5%.
Any money earned above $40,000 is taxed at 7%.
The income tax for Aribraska is modeled by a piecewise defined function.
Over which part of the domain is the piecewise function defined as
f(x) = 0.05x – 300?






An Aribraska resident who earns $32,000 would owe how much in tases?

$1,300

$1,600

$1,740

Answer 1

The piecewise function is defined as f(x) = 0.05x - 300 over the income range of $15,000 to $40,000. An Aribraska resident who earns $32,000 would owe $1,600 in taxes.

Step-by-step explanation:

The piecewise function is defined as f(x) = 0.05x - 300 over the part of the domain where the income is between $15,000 and $40,000. This is because the tax rate of 5% is being applied to the income in this range. For any income above $40,000, the tax rate is 7%, so the function would not be equal to 0.05x - 300.

To calculate the amount of taxes owed by an Aribraska resident who earns $32,000, we need to determine the income range that applies to this amount. Since $32,000 is within the range of $15,000 to $40,000, we can use the piecewise function to calculate the taxes:

f(32,000) = 0.05(32,000) - 300 = 1,600

Therefore, an Aribraska resident who earns $32,000 would owe $1,600 in taxes.

Answer 2

$1300

Step-by-step explanation: