Math  /  Algebra

QuestionA state's income tax for a single person in a recent year was determined by the rule below, where x is the person's taxable income. h(x)={0.03x, if 0x<5000150+0.04(x5000), if 5000x<11,000390+0.05(x11,000), if x11,000h(x)=\left\{\begin{array}{ll} 0.03 x, & \text { if } 0 \leq x<5000 \\ 150+0.04(x-5000), & \text { if } 5000 \leq x<11,000 \\ 390+0.05(x-11,000), & \text { if } x \geq 11,000 \end{array}\right.
Find the following function values and interpret the answers. (a) h(2270)h(2270) (b) h(6420)h(6420) (c) h(42,650)h(42,650)

Studdy Solution
Calculate h(42,650) h(42,650) :
h(42,650)=390+0.05(42,65011,000) h(42,650) = 390 + 0.05(42,650 - 11,000)
h(42,650)=390+0.05×31,650 h(42,650) = 390 + 0.05 \times 31,650
h(42,650)=390+1582.5 h(42,650) = 390 + 1582.5
h(42,650)=1972.5 h(42,650) = 1972.5
Interpretation: For a taxable income of 42,650,theincometaxis42,650, the income tax is 1972.50.
The function values are: (a) h(2270)=68.1 h(2270) = 68.1 (b) h(6420)=206.8 h(6420) = 206.8 (c) h(42,650)=1972.5 h(42,650) = 1972.5

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