SOLUTION: (6 pts) A particular state computed income tax, T (in dollars) on a person’s income, x (in dollars), by the following formula: T (x) ={0.018x if 0 ≤ x ≤ 5,

Question 1134070: (6 pts) A particular state computed income tax, T (in dollars) on a person’s income, x (in dollars), by the following formula:
T (x) ={0.018x if 0 ≤ x ≤ 5,000
90+ 0.025 (x-5,000) if 5,000 < x < 10,000
215 +0.050 (x-10,000) if x > 10,000
What is the tax on an income of $7,300? Show work.

(b) What is the tax on an income of $73,000? Show work.

Found 2 solutions by mananth, math_tutor2020:
Answer by mananth(16946) (Show Source): You can put this solution on YOUR website!

A particular state computed income tax, T (in dollars) on a person’s income, x (in dollars), by the following formula:

T (x) ={0.018x if 0 ≤ x ≤ 5,000
90+ 0.025 (x-5,000) if 5,000 < x < 10,000
215 +0.050 (x-10,000) if x > 10,000
What is the tax on an income of $7,300? Show work.
T (x) ={0.018x if 0 ≤ x ≤ 5,000
T(x) = ( 0.018*5000)= 90
90+ 0.025 (x-5,000) if 5,000 < x < 10,000
7300 - 5000 = 2300
90+0.025(2300) = $147.5 on $7300 income
(b) What is the tax on an income of $73,000? Show work.
Use same method tocalculate for $73000

Answer by math_tutor2020(3817) (Show Source): You can put this solution on YOUR website!

Part (a)

x = income amount in dollars
T(x) = income tax in dollars

x = 7300 fits the interval 5000 < x < 10000, which means we'll use the second part of the piecewise function.

T(x) = 90 + 0.025(x-5000) when 5000 < x < 10000
T(7300) = 90 + 0.025(7300-5000)
T(7300) = 147.50

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Part (b)

x = 73,000 fits the interval x > 10,000.

T(x) = 215 + 0.050(x-10000) when x > 10,000
T(73000) = 215 + 0.050(73000-10000)
T(73000) = 3365

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Answers:
(a) $147.50
(b) $3365

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