Question

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 \( m = 2 \).