Question

A state income tax law reads as follows:

Write a piecewise-defined function to
represent the income tax law.
Annual Income (dollars)
< $2000
$2000-$6000
> $6000
Tax
$0 tax
2% of income over $2000
$80 plus 5% of income
over $6000

Answer 1

The state income tax law can be modeled with a piecewise-defined function that calculates the tax based on income ranges, reflecting an increasing tax amount and tax rate with higher income brackets.

Step-by-step explanation:

To represent the state income tax law as given in piecewise-defined function, we divide the function based on the specified income ranges. The tax function T(I) for an income I can be modeled as follows:

For I < $2000: T(I) = $0

For $2000 ≤ I ≤ $6000: T(I) = 0.02 × (I - $2000)

For I > $6000: T(I) = $80 + 0.05 × (I - $6000)

This function reflects the increase in taxes as income increases, as well as the change in the slope of the tax rate at higher levels of income. This is analogous to the progression in tax brackets observed in government programs indexed to inflation.

Answer 2

Step-by-step explanation: