Under a certain law, the first p30,000.00 of earnings are aubjected to 12% tax, earning greater than p30,000.00 and up to p50,000.00 are subjected to 15% tax,and earnings greater than p50,000.00 are taxed at 20% .write a piecewise function that models this situation.
Answers
Given : Under a certain law, the first p30,000 of earnings are subjected to 12% tax, earning greater than p30,000 and up to p50,000. are subjected to 15% tax ,and earnings greater than p50,000 are taxed at 20%
To Find : .write a piecewise function that models this situation.
Solution:
the first p30,000 of earnings are subjected to 12% tax
Earning can not be less than 0
Earning = E
Hence 0 <E ≤30,000
Tax = (12/100)E = 0.12E
Tax for 30,000 = 0.12 * 30,000 = 3600
15% tax, earning greater than p30,000 and up to p50,000
=> 30,000 <E ≤50,000
3600 + 0.15 (E - 30,000) = 0.15E - 900
Tax for 50,000 = 0.15(50000) - 900 = 6600
20% tax, earning greater than p50,000
=> 50000 < E
6600 + 0.2 (E - 50,000) = 0.2E - 3400
piecewise function that models this situation.
0.12E 0 <E ≤30,000
0.15E - 900 30,000 <E ≤50,000
0.2E - 3400 50000 < E
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