Im currently writing an assignment in my math class. I have to calculate the amount of money an individual pays in taxes, based on his income.
Where I live (Denmark), if you earn more than 500.000DKK you will be charged an additional 7% in taxes for all money made above the 500.000DKK, and the regular 35%, for the rest. (Not actual numbers)
This is the best I could express the formula using my high school math:
MoneyIPayOf(income) = (income <= 500.000) ? (income * 0.35) : (500.000 * 0.35 + (income - 500.000) * 0.42)
Even I can see this formula makes no sense, but I have no idea how to formulate it in math, without the silly looking and programming inspired conditional statement.
How I hope people would read it is:
MoneyIPayOf(600.000) = (600.000 <= 500.000) : (500.000 * 0.35 + (600.000 - 500.000) * 0.42)
MoneyIPayOf(400.000) = (400.000 <= 500.000) : (400.000 * 0.35)
How could I write this formula properly, so real mathmaticians could understand it?
You could try to use something like
max{(income - 500.000), 0}if you want an expression without an explicit conditional. Thus, when the income is lower than $500.00$, this term evaluates to $0$, which will not change the amount of the second case.Anyways, mathematicians are used to conditional statements. You could write something like
$\text{MoneyIPayOf(income)}=\begin{cases}\text{formula 1} & \text{if income}\leq 500.000\\\text{formula 2}&\text{if income}\geq 500.000\end{cases}$