Question

A phone company charges for service according to the formula: C(n)=23+0.1n, 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 :
Minutes
Dollars
Dollars per Minute
Minutes per Dollar
The initial value in this equation is :
Minutes per Dollar
Dollars per Minute
Dollars
Minutes

Answer 1

To analyze the given formula \( C(n) = 23 + 0.1n \), we can determine both the rate of change and the initial value:

1. **Rate of Change**:
The "rate of change" in the context of this equation refers to the coefficient of \( n \), which is \( 0.1 \). This coefficient represents the increase in monthly charge (in dollars) for each additional minute talked. Therefore, the rate of change is measured in:

**Dollars per Minute**.

2. **Initial Value**:
The "initial value" in a linear function is typically the constant term (the value of the function when \( n = 0 \)). Here, when no minutes are talked (\( n = 0 \)), the charge is:

\( C(0) = 23 + 0.1 \times 0 = 23 \).

This means that the initial value is:

**Dollars**.

In summary:
- The rate of change is **Dollars per Minute**.
- The initial value is **Dollars**.