the taxpayer should pay 6% of his total income if his income amounts to PHP 500,000 and PHP 1,000,000, the taxpayer should pay 8% of the total income. If the income is PHP 1,000,000 or more, he should pay 9.5% of the total income. Express the tax as a function of x for any PHP x income.
Please help me and kindly put the solution too. Thank you very much :)
Sure! To express the tax as a function of x for any PHP x income, we need to consider the different tax rates for different income ranges.
Let's break it down:
- For incomes less than or equal to PHP 500,000, the taxpayer should pay 6% of the total income.
- For incomes between PHP 500,000 and PHP 1,000,000, the taxpayer should pay 8% of the total income.
- For incomes PHP 1,000,000 or more, the taxpayer should pay 9.5% of the total income.
To express the tax as a function of x, we can create a piecewise function that accounts for these different income ranges.
Let's define the function as "tax(x)":
tax(x) =
6% of x if x <= 500,000
8% of x if 500,000 < x <= 1,000,000
9.5% of x if x > 1,000,000
Now, let's solve the problem using the equation. We'll calculate the tax for different income values:
For example:
1. If x = PHP 300,000 (income less than or equal to 500,000):
tax(x) = 6% of 300,000 = (6/100) * 300,000 = PHP 18,000
2. If x = PHP 750,000 (income between 500,000 and 1,000,000):
tax(x) = 8% of 750,000 = (8/100) * 750,000 = PHP 60,000
3. If x = PHP 1,200,000 (income greater than 1,000,000):
tax(x) = 9.5% of 1,200,000 = (9.5/100) * 1,200,000 = PHP 114,000
Please note that this function assumes that the tax is calculated on the total income itself.
Hope this helps!