A phone company charges for service according to the formula:
C
(
n
)
=
12
+
0.07
n
C
(
n
)
=
12
+
0.07
n
, where
n
n
is the number of minutes talked, and
C
(
n
)
C
(
n
)
is the monthly charge, in dollars.

The rate of change in this equation is:  Correct

The initial value in this equation is:

The given equation for the phone company's charge is:

\[
C(n) = 12 + 0.07n
\]

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

### 1. **Rate of Change**
The rate of change in this equation is represented by the coefficient of $ n $, which is **0.07**. This means that for every additional minute talked, the charge increases by $0.07.

### 2. **Initial Value**
The initial value in this equation is the constant term, which is **12**. This represents the fixed monthly charge before any minutes are used.

So, the answers are:
- **Rate of change**: 0.07 (dollars per minute)
- **Initial value**: 12 dollars

Would you like further clarification or more details?

### 5 Related Questions
1. What would be the monthly cost if 100 minutes are used?
2. How does the monthly charge change if the rate per minute increases to 0.10 dollars?
3. Is this a linear relationship, and how can we tell?
4. What does the slope of the line represent in this context?
5. If the initial charge changes to 15 dollars, how would that affect the equation?

### Tip:
To identify the rate of change in linear equations like this one, look for the coefficient of the variable (in this case, $ n $). The initial value is the constant term.

A phone company charges for service according to the formula: C(n) = 12 + 0.07n, where n is the number of minutes talked, and C(n) is the monthly charge in dollars. The rate of change in this equation is: Correct. The initial value in this equation is:

Understand how to calculate monthly service charges using the linear equation C(n) = 12 + 0.07n, where 12 represents the base charge and 0.07 is the cost per minute. Learn how to identify the rate of change and initial value in this equation, suitable for Grades 6-8.

Math Problem Statement

A phone company charges for service according to the formula: C ( n )

12 + 0.07 n C ( n )

Solution

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