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The equation given is:

\[
C(n) = 11 + 0.05n
\]

Where:
- $ C(n) $ is the monthly charge in dollars,
- $ n $ is the number of minutes talked.

### 1. **Rate of Change:**
The rate of change is represented by the coefficient of $ n $, which is the value that multiplies $ n $. In this case, the coefficient of $ n $ is **0.05**. This means that for every additional minute talked, the charge increases by **$0.05**.

### 2. **Initial Value:**
The initial value is the constant term in the equation, which represents the charge when no minutes are talked (i.e., when $ n = 0 $). Here, the initial value is **$11**.

#### Answers:
- **Rate of change**: 0.05 (this represents the additional charge per minute)
- **Initial value**: 11 (this is the base charge even if no minutes are talked)

Would you like more details on how these were determined? Here are five related questions:

1. What does the rate of change represent in a linear equation in general?
2. How would the initial value affect the total cost if the rate of change increased?
3. If the rate of change was 0.10, how would the equation differ?
4. How would you interpret the equation if the initial value were $0?
5. Can the rate of change in a real-life scenario like this be negative?

**Tip:** The rate of change in an equation describes how quickly one variable (like cost) changes with respect to another variable (like minutes talked).

A phone company charges for service according to the formula: C(n) = 11 + 0.05n, where n is the number of minutes talked, and C(n) is the monthly charge, in dollars.

Learn how to calculate the rate of change and initial value from the linear equation C(n) = 11 + 0.05n, representing a phone company's service charges. This tutorial explains the concept of rate of change and how to determine the base cost of a service.

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