Step Function Intuition Math Example 2

Solution

1. 1
   Model: first hour costs \3$, each additional started hour costs$\$2$. For $t>1$: $C(t) = 3 + 2\lceil t-1\rceil$ where $\lceil \cdot \rceil$ is the ceiling function.
2. 2
   Evaluate: C(0.5) = \3$(within first hour);$C(1) = \$3$; C(1.2) = 3+2\cdot 1 = \5$(one additional hour started);$C(3.9) = 3 + 2\cdot 3 = \$9$ (three additional hours started).
3. 3
   The cost function is a step function — constant on intervals, jumping at integer boundaries.