Question

a phone company charges for service according to the formula: (c(n) = 10 + 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 per dollar

the initial value in this equation is: select an answer

Explanation:

⚡ Using what you learned: slope-intercept and standard form

Step 1: Identify the Rate of Change

The given cost function is:

$$ C(n) = 10 + 0.1n $$

This is a linear equation in the form \( y = mx + b \) (or \( C(n) = mn + b \)), where:

• \( m \) is the rate of change (slope).
• \( b \) is the initial value (\( y \)-intercept).

The coefficient of \( n \) is \( 0.1 \).

The units for the rate of change are the units of the output divided by the units of the input:

$$ \text{Units} = \frac{\text{Dollars}}{\text{Minute}} $$

• Rate of change: 0.1
• Unit: Dollars per Minute

Step 2: Identify the Initial Value

The constant term in the equation is \( 10 \). This represents the cost when the number of minutes talked, \( n \), is \( 0 \).

The units for the initial value are the same as the output variable, \( C(n) \), which is in dollars.

• Initial value: 10
• Unit: Dollars

Answer:

• The rate of change in this equation is: 0.1 with units Dollars per Minute
• The initial value in this equation is: 10 with units Dollars