A certain country taxes the first $22,000 of an individual’s income at a rate of 10%, and all income over $22,000 is taxed at 25%. Find a pi

Question

A certain country taxes the first $22,000 of an individual’s income at a rate of 10%, and all income over $22,000 is taxed at 25%. Find a piecewise-defined function T that specifies the total tax on an income of x dollars. (Simplify your answer completely.)

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Piper 2 months 2021-09-26T05:48:51+00:00 1 Answer 0 views 0

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    2021-09-26T05:49:59+00:00

    Answer:

    T = {$0.01a     if a ≤ $22000

          $(0.25a – 3300)    if a > $22000}

    Step-by-step explanation:

    A country taxes the first $22000 of an individual’s income at 10%.

    If the income of an individual is = $a.

    Tax up-to $22000 will be

    = a × \frac{10}{100}

    = $0.01a

    Above $22000 tax deducted will be

    = (a – 22000)×\frac{25}{100}

    = 0.25a – 5500

    = $(0.25a – 5500)

    Total tax ‘T’ = 0.25a – 5500 + 2200

    T = $(0.25a – 3300)

    Piece-wise function will be  

    T = {$0.01a     if a ≤ $22000

          $(0.25a – 3300)    if a > $22000}

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