Step functions are fascinating mathematical functions that remain constant over intervals and then jump to a new constant value. They can be found in various everyday situations. Here are two examples:
1. Electricity Billing: In many regions, electricity providers charge customers based on tiered rates. For instance, the first 100 kilowatt-hours (kWh) might be charged at a lower rate, the next 100 kWh at a higher rate, and so on. This creates a step function where the cost of electricity jumps at specific consumption thresholds. For example:
- 0-100 kWh: $0.10 per kWh
- 101-200 kWh: $0.15 per kWh
- 201+ kWh: $0.20 per kWh
This means that as your usage increases into a new tier, the cost per kWh steps up suddenly at the defined limits.
2. Tax Brackets: Personal income tax systems in many countries utilize step functions when determining tax liability. Tax brackets are set ranges of income that are taxed at differing rates. For example:
- 0 – $10,000: 10%
- $10,001 – $40,000: 20%
- Above $40,000: 30%
Here, if your income increases and moves into a higher tax bracket, your tax rate jumps to the new rate at that specific income threshold, creating a step-like function in how your tax is calculated.
These examples illustrate how step functions can effectively represent scenarios in daily life, reflecting how certain rates or charges change at defined intervals.