Question

Under a certain Law, the first P30,000.00 of earnings are subjected to 12% tax,earning greater than P30,000.00 and up to 50,000.00 are subjected to 15% tax, andearnings greater than 50,000.00 are taxed at 20%. Write a piecewise function thatmodels this situation.​

Answer 1

To model the situation of different tax rates based on earnings, a piecewise function can be used. The function will have three parts, each representing a different tax rate based on the earnings threshold. The function will be y = 0.12 * x for earnings up to 30,000, y = 0.15 * (x - 30,000) + 0.12 * 30,000 for earnings between 30,000 and 50,000, and y = 0.20 * (x - 50,000) + 0.15 * (50,000 - 30,000) + 0.12 * 30,000 for earnings above 50,000.

Step-by-step explanation:

To model the situation described, we can create a piecewise function that represents the different tax rates based on earnings. Let's call the earnings 'x' and the tax rate 'y'.

If x is less than or equal to 30,000, the tax rate is 12%. So, we can write this part of the function as y = 0.12 * x.

If x is greater than 30,000 and less than or equal to 50,000, the tax rate is 15%. So, we can write this part of the function as y = 0.15 * (x - 30,000) + 0.12 * 30,000.

If x is greater than 50,000, the tax rate is 20%. So, we can write this part of the function as y = 0.20 * (x - 50,000) + 0.15 * (50,000 - 30,000) + 0.12 * 30,000.