Let's carefully analyze the given formula to understand how the charges are calculated. The formula provided by the phone company is:
[tex]\[ C(n) = 22 + 0.03n \][/tex]
where:
- [tex]\( C(n) \)[/tex] represents the monthly charge in dollars,
- [tex]\( n \)[/tex] represents the number of minutes talked.
### Step-by-Step Solution:
1. Identifying the Rate of Change:
The term [tex]\( 0.03n \)[/tex] represents the variable part of the equation, where [tex]\( 0.03 \)[/tex] is the coefficient of [tex]\( n \)[/tex]. This coefficient indicates the rate at which the charge increases per minute talked. Specifically, for each additional minute that you talk, the cost increases by $0.03.
Therefore, the rate of change in the equation is:
[tex]\[ 0.03 \][/tex]
2. Identifying the Initial Value:
In the given formula, the constant term [tex]\( 22 \)[/tex] is the value that does not depend on the number of minutes talked. This represents the base charge or the fixed monthly charge, regardless of the number of minutes talked.
Therefore, the initial value in the equation is:
[tex]\[ 22 \][/tex]
To summarize:
- The rate of change in this equation is: [tex]\( 0.03 \)[/tex]
- The initial value in this equation is: [tex]\( 22 \)[/tex]
This comprehensive breakdown allows us to understand how the provided formula dictates the charges based on the number of minutes talked, with the rate of change denoting the per-minute cost and the initial value representing the fixed base charge.
