E X P = { <mtable columnalign="left left" rowspacing=".2em" columnspacing

Question

E X P = {\begin{cases} n^{3} (\frac{⌊ \frac{n + 1}{3} ⌋ + 24}{50}) & n \leq 15 \\ n^{3} (\frac{n + 14}{50}) & 15 \leq n \leq 36 \\ n^{3} (\frac{⌊ \frac{n}{2} ⌋ + 32}{50}) & 36 \leq n \leq 100 \end{cases}

In this equation there are 3 systems of equations, but there are inequalities next to them. Does this mean that for example we use the top equation when

n \leq 15

and so on?

Answer 1

Yes, you are correct, that's exactly what that means. This is an example of a piecewise function. The idea is that sometime, as in this case, it's useful to have a different rule for assigning outputs depending on the value of the input.