In this scenario, we can define the variables for the entrance fee and the cost of ride tickets:
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Initial Value (b): The initial value represents the fixed cost that everyone incurs before they start going on rides. This is the entrance fee, which is $12. So, we have:
\[ b = 12 \]
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Rate of Change (m): The rate of change represents how much the total cost increases for each additional ride taken. Since the cost of each ride ticket is $2, this means that for every ride taken, the total cost increases by $2. So, we have:
\[ m = 2 \]
So the answers are:
- The initial value is \( b = 12 \)
- The rate of change is \( m = 2 \)