Taxes The table below shows some sample incomes and the income tax due for each taxable income.
a. Can a linear function model exactly the points from the table? Explain.
b. If so, find a linear function T = f (x) that models the points.
c. Verify that the model fits the data by evaluating the function at x = 30,100 and x = 30,300 and comparing the resulting T-values with the income tax due for these taxable incomes.
d. If the model can be interpreted continuously, use it to find the tax due on taxable income of $30,125. Is this an interpolation or an extrapolation from the data?
e. Can this model be used to compute all tax due on taxable income?
Taxable Income | Income Tax Due |
$30,000 | $3665.00 |
30,050 | 3672.50 |
30,100 | 3680.00 |
30,150 | 3687.50 |
30,200 | 3695.00 |
30,250 | 3702.50 |
30,300 | 3710.00 |
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