Question

A water company charges residential customers a quarterly flat fee of $25 for up to 5000 gallons of water. The company charges $10 per thousand for the first 10,000 gallons of water after the minimum allowance. The next 10,000 gallons is $5 per thousand. All other consumption over 25,000 gallons is $2.50 per thousand.

a. Write a piecewise function w(x) that can be used to determine a customer's quarterly bill for using x gallons o water. On average, a family of four consumes 247.2 gallons of water per day. Calculate the quarterly water bill for a family of four. Explain how you determined your answer

Answer 1

The function w(x) for determining a customer's quarterly water bill can be defined using a piecewise approach. For a family of four with an average daily consumption of 247.2 gallons, the quarterly water bill is $444.70.

Step-by-step explanation:

The function w(x) that can be used to determine a customer's quarterly bill for using x gallons of water can be defined using a piecewise approach.

For the first 5000 gallons, the flat fee of $25 applies. So, if x ≤ 5000, the bill will be $25.

For the next 10,000 gallons (5000 < x ≤ 15,000), the charge is $10 per thousand gallons. This can be calculated as ((x - 5000) / 1000) * 10.

For the next 10,000 gallons (15,000 < x ≤ 25,000), the charge is $5 per thousand gallons. This can be calculated as ((x - 15,000) / 1000) * 5.

For any consumption over 25,000 gallons (x > 25,000), the charge is $2.50 per thousand gallons. This can be calculated as ((x - 25,000) / 1000) * 2.50.

To calculate the quarterly water bill for a family of four, we need to know their average daily consumption. Given that a family of four consumes 247.2 gallons of water per day on average, we can multiply it by 91 (number of days in a quarter) to get the total consumption for the quarter. Substituting this value in the piecewise function will give us the bill.

Using the given information:

1. For the first 5000 gallons, the bill is $25.
2. For the next 10,000 gallons, the bill is ((15,000 - 5000) / 1000) * 10 = $100.
3. For the next 10,000 gallons, the bill is ((25,000 - 15,000) / 1000) * 5 = $50.
4. For the remaining 107,880 gallons (247.2 * 91 - 25,000), the bill is ((107,880) / 1000) * 2.50 = $269.70.

Adding these amounts together, the quarterly water bill for a family of four will be $25 + $100 + $50 + $269.70 = $444.70.

Therefore, the quarterly water bill for a family of four is $444.70.