To determine if the cost of visiting the outdoor swimming pool is proportional to the total number of days visited, we can analyze the cost structure.
- The yearly registration fee is a fixed cost of $25, which is incurred regardless of the number of days you visit the pool.
- The cost to visit the pool is $8 per day.
The total cost \( C \) for visiting the pool for \( d \) days can be expressed as:
\[ C = 25 + 8d \]
In a proportional relationship, the cost would be directly related to the number of days with no fixed cost. This means that for a situation to be proportional, the relationship should be of the form \( C = kd \), where \( k \) is a constant.
In our case, the equation \( C = 25 + 8d \) indicates that there is an additional constant ($25) added to the cost based on the number of days visited. Thus, the total cost is not solely reliant on the days visited; it includes a fixed registration cost.
Therefore, since the total cost is affected by a fixed registration fee and cannot be expressed in the form \( C = kd \) without that additional constant, the cost is not proportional to the total number of days visited.