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.)


*E*(*x*) = 
 
    if 0 ≤ *x* ≤ 300 
 
    if 300 < *x*



(b) Graph the function *E* for 

0 ≤ *x* ≤ 600.

Here's the graph of the monthly cost function $ E(x) $ for electricity usage between 0 and 600 kWh. The function has two distinct segments:

1. **For $ 0 \leq x \leq 300 $**: The cost increases at a rate of $0.15 per kWh.
2. **For $ x > 300 $**: The cost increases at a reduced rate of $0.04 per kWh after an initial cost of $40.00.

This graph visually demonstrates how the cost increases more slowly after 300 kWh due to the lower rate applied to additional usage.

Would you like more details or have any questions?

Here are some related questions for further exploration:
1. What is the exact cost when a customer uses 600 kWh?
2. How much does the cost increase between 200 kWh and 400 kWh of usage?
3. If the rate for usage over 300 kWh were increased to $0.10 per kWh, how would the graph change?
4. Determine the monthly cost if a customer only uses 150 kWh.
5. What happens to the monthly cost as the usage approaches 1000 kWh?

**Tip:** Understanding how different pricing schemes affect total costs can help in managing energy usage and expenses efficiently.

Understand how to calculate the monthly electricity cost using a piecewise function based on usage. This problem involves determining costs up to 600 kWh, including rates per kWh and fixed base charges. Explore the graph and learn about managing electricity expenses effectively.

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