Determine the initial value and the rate of change in the following description. At a local festival, the entrance fee is $12 per person, and ride tickets cost $2 for every ride. The initial value is b= , and the rate of change is m= .

Answer 1

In the context of the described situation, where the entrance fee is a fixed cost and ride tickets cost a specific amount per ride, we can determine the initial value and the rate of change in terms of a cost function.

1. Initial Value (b): The initial value \( b \) represents the fixed cost before any additional variable costs are added. In this case, the entrance fee is \( $12 \), which is the initial cost incurred before purchasing any ride tickets. Therefore, the initial value is:

   \[ b = 12 \]

2. Rate of Change (m): The rate of change \( m \) represents the additional cost incurred for each ride taken. Here, the cost per ride ticket is \( $2 \). Thus, for each ride, the total cost increases by \( $2 \). This means that the rate of change is:

   \[ m = 2 \]

In summary:

• The initial value is \( b = 12 \).
• The rate of change is \( m = 2 \).