Westside Energy charges its electric customers a base rate of $7.00 per month, plus 15¢ per kilowatt-hour (kWh) for the first 300 kWh used and 4¢ per kWh for all usage over 300 kWh. Suppose a customer uses x kWh of electricity in one month.
(a) Express the monthly cost E as a piecewise defined function of x. (Assume E is measured in dollars.)
(b) Graph the function E for 0 ≤ x ≤ 600

Here's the graph of the monthly cost function $ E(x) $ for $ 0 \leq x \leq 600 $ kWh:

- The first segment represents the cost for usage up to 300 kWh, where the cost increases linearly at a rate of $0.15 per kWh.
- The second segment starts at 300 kWh, where the rate of increase slows to $0.04 per kWh, reflecting the lower rate for usage beyond 300 kWh.

Would you like more details on this function or have any questions?

Here are 5 related questions to expand your understanding:

1. How would the piecewise function change if the base rate was increased to $10.00 per month?
2. What would the monthly cost be if a customer used 450 kWh in a month?
3. How does the slope of the graph change after 300 kWh, and what does that represent?
4. If a customer reduces their usage from 400 kWh to 250 kWh, how much would they save?
5. How would the graph change if the cost for usage over 300 kWh increased to $0.05 per kWh?

**Tip:** Understanding piecewise functions is crucial when dealing with rates that change based on usage, such as tiered billing systems in utilities.

Explore how to calculate the monthly electricity cost using a piecewise function for Westside Energy's billing system. Understand the cost structure based on usage tiers and rates per kilowatt-hour. Includes a graph and detailed explanations.

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