The formula for the average rate of change between two points on a line is:

ARC

=

Δ

𝐶

(

𝑥

)

Δ

𝑥

ARC= 

Δx

ΔC(x)

​
 
Where:

Δ

𝐶

(

𝑥

)

ΔC(x) is the change in cost.

Δ

𝑥

Δx is the change in the number of units.

But because this is a linear function, the rate of change is constant, and it equals 0.78 dollars per unit of electricity. This means:

For every additional unit of electricity you consume, your bill increases by $0.78.

Since the fixed charge is always there, the average rate of change only depends on the variable part of the linear function, which is $0.78/unit. So, the more electricity you use, the bigger impact that $0.78/unit will have on your total bill

The formula for the **Average Rate of Change (ARC)** between two points on a line is given by:

\[
\text{ARC} = \frac{\Delta C(x)}{\Delta x}
\]

Where:
- $\Delta C(x)$ is the change in cost.
- $\Delta x$ is the change in the number of units (in this case, units of electricity).

Because this is a **linear function**, the rate of change is constant, meaning it doesn't vary with different values of $x$. In your case, the rate of change is provided as **0.78 dollars per unit**, which implies that for every additional unit of electricity consumed, the bill increases by \$0.78. 

This constant rate of 0.78 only affects the **variable part** of the cost, as there is also a fixed charge component that remains the same regardless of usage. As a result, the more electricity you use, the larger the variable portion of the bill becomes due to the cumulative impact of the \$0.78 per unit rate.

To summarize:
- **Fixed charge**: remains constant, unrelated to usage.
- **Variable charge**: \$0.78/unit, directly related to the number of units consumed.
  
The total bill increases linearly as more electricity is used, with the average rate of change only reflecting the variable cost per unit.

### Would you like more details or have any questions?

### Related questions:
1. How do you calculate the total cost if the number of units and the fixed charge are known?
2. What is the difference between a linear function and a non-linear function in terms of rates of change?
3. How would you calculate the average rate of change if the cost per unit wasn't constant?
4. How does the fixed charge impact the overall cost compared to the variable charge?
5. Can the average rate of change apply to other utility bills or only electricity?

### Tip: When analyzing costs, break down fixed and variable components to understand how consumption impacts total expenses!

The formula for the average rate of change between two points on a line is: ARC = ΔC(x)/Δx, where ΔC(x) is the change in cost and Δx is the change in the number of units. Since this is a linear function, the rate of change is constant and equals 0.78 dollars per unit of electricity. For every additional unit consumed, the bill increases by $0.78. The average rate of change only depends on the variable part of the function, $0.78/unit.

Understand the average rate of change formula (ARC = ΔC(x)/Δx) with a real-world example involving electricity costs. Learn how a constant rate of $0.78 per unit of electricity impacts your total bill. This explanation covers the concepts of linear functions and the relationship between fixed and variable costs, suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation