Chapter 1.3, Problem 110PE

Here is the Federal Tax Rate Schedule X that species the tax owed by a single taxpayer for a recent year.

If Your Taxable Income b Over	But Mot Over	The Tax You Ooe Is	Of the Amount Over
$ 0	$ 8500	10%	$ 0
$ 8500	$ 34,500	[Math Processing Error]	$ 8500
$ 34,500	$ 83,600	[Math Processing Error]	$ 34,503
$ 83,600	$ 174,400	$ 17,025.00 + 28%	$ 83,603
$174,400	$379,150	$ 42, 449.00 + 33%	$ 174,400
$ 379,150	-	$110,016.50 + 35%	$379 150

The preceding -.ax table can be modeled by a piecewise function, where x represents the taxable income ot a single taxpayer and T(x) is the tax owed

$T(x)=\{\begin{array}{l}\begin{array}{ccc}0.10x& \text{if}& 0<x\le 8500\end{array}\\ \begin{array}{ccc}850.00+0.25x(x-34,500)& \text{if}& 8500<x\le 34,500\end{array}\\ \begin{array}{ccc}4750.00+0.25(x-34,500)& \text{if}& 34,500<x\le 83,600\end{array}\\ \begin{array}{ccc}17,025.00+0.28(x-83,600)& \text{if}& 83,600<x\le 174,400\end{array}\\ \begin{array}{ccc}\underset{\_}{?}& \text{if}& 174,400<x\le 379,150\end{array}\\ \begin{array}{ccc}\underset{\_}{?}& \text{if}& x>379,150.\end{array}\end{array}$

In Exercises 109-110, refer to the preceding tax table.

Find the algebraic expression for the missing piece of T(z) that models tax owed for the domain $(379,150,\infty )$.