Question

Suppose a state's income tax code states that tax liability is 12% on the first $20,000 of taxable earnings and 16% on the remainder. By hand, find constants a and b for the tax function T(x) = { a + 0.12x if x ? 20,000; b + 0.16(x - 20000) if x > 20,000 such that lim(x?0+) T(x) = 0 and T(x) is continuous at x = 20,000. Why is it important for these 2 conditions to hold (state 2 reasons in context of the application)? Plot this piecewise function in Maple.

Name: Suppose a state's income tax code states that tax liability is 12% on the first $20,000 of taxable earnings and 16% on the remainder. By hand, find constants a and b for the tax function T(x) = { a + 0.12x if x ? 20,000; b + 0.16(x - 20000) if x > 20,000 such that lim(x?0+) T(x) = 0 and T(x) is continuous at x = 20,000. Why is it important for these 2 conditions to hold (state 2 reasons in context of the application)? Plot this piecewise function in Maple.
Uploaded: 2023-03-25T18:35:21-08:00
Duration: 1 min 37 s
Channel: Andrew Noble

          Suppose a state's income tax code states that tax liability is 12% on the first $20,000 of taxable earnings and 16% on the remainder. By hand, find constants a and b for the tax function T(x) = { a + 0.12x if x ? 20,000; b + 0.16(x - 20000) if x > 20,000 such that lim(x?0+) T(x) = 0 and T(x) is continuous at x = 20,000. Why is it important for these 2 conditions to hold (state 2 reasons in context of the application)? Plot this piecewise function in Maple.

Suppose a state's income tax code states that tax liability is 12% on the first $20,000 of taxable earnings and 16% on the remainder. By hand, find constants a and b for the tax function T(x) = { a + 0.12x if x ? 20,000; b + 0.16(x - 20000) if x > 20,000 such that lim(x?0+) T(x) = 0 and T(x) is continuous at x = 20,000. Why is it important for these 2 conditions to hold (state 2 reasons in context of the application)? Plot this piecewise function in Maple.

Added by Lori T.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Andrew Noble

03/25/2023

Step 1

12x \) for $ x < 20000 $, we can substitute x = 0 into the equation: \[ a + 0.12(0) = 0 \] \[ a = 0 \] Therefore, the value of constant a is 0. ** Show more…

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Suppose a state's income tax code states that tax liability is 12% on the first $20,000 of taxable earnings and 16% on the remainder. By hand, find constants a and b for the tax function T(x) = { a + 0.12x if x ≤ 20,000, b + 0.16(x - 20000) if x > 20,000, such that lim(x→0+) T(x) = 0 and T(x) is continuous at x = 20,000. Why is it important for these 2 conditions to hold (state 2 reasons in context of the application)? Plot this piecewise function in Maple.