An outdoor swimming pool costs $8 per day to visit during the summer. There is also a $25 yearly registration fee. Is the cost proportional to the total number of days visited?

Answer 1

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.

1. The yearly registration fee is a fixed cost of $25, which is incurred regardless of the number of days you visit the pool.
2. 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.