With aging, body fat increases and muscle mass declines. The line graphs show the percent body fat in adult women and men as they age from 25 to 75 years. Use the graphs to solve Exercises.
Source: Thompson et al., The Science of Nutrition , Benjamin Cummings, 2008
The function p(x) = −0.004x2 + 0.25x + 33.64 models percent body fat, p(x), where x is the number of years a person’s age exceeds 25. Use the graphs to determine whether this model describes percent body fat in women or in men.
Here is the 2011 Federal Tax Rate Schedule X that specifies the tax owed by a single taxpayer.
If Your Taxable Income Is Over | But Not Over | The Tax You Owe Is | Of the Amount Over |
$ 0 | $ 8500 | 10% | $ 0 |
$ 8500 | $ 34,500 | $ 850.00 + 15, | $ 8500 |
$ 34,500 | $ 83,600 | $ 4750.00 + 25, | $ 34,500 |
$ 83,600 | $174,400 | $ 17,025.00 + 28, | $ 83,600 |
$174,400 | $379,150 | $ 42,449.00 + 33, | $174,400 |
$379,150 | — | $110,016.50 + 35, | $379,150 |
The preceding tax table can be modeled by a piecewise function, where x represents the taxable income of a single taxpayer and T (x) is the tax owed:
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