To determine which model best fits the data represented in the scatterplot, we need to consider the general trends often observed in values over time, particularly for items like basketball cards.
-
Linear Model: This would imply that the value of the basketball cards increases or decreases at a constant rate. While some individual cards may have steady value over time, it's unlikely that all cards would follow this trend perfectly; card values often vary based on demand, rarity, and other factors.
-
Quadratic Model: This suggests a parabolic trend, where card values might initially increase or decrease before reversing trend. This model can represent situations where growth accelerates over time but may not be ideal for capturing the value change consistently.
-
Exponential Model: This would imply that the value of basketball cards increases (or decreases) at a rate proportional to their current value, leading to rapid increases over time. Card values commonly experience spikes due to trends, player performance, or other factors, making an exponential model a possible candidate.
-
No Model: This could be an option if the data appears too random to fit into a specific trend.
Without seeing the actual scatterplot or knowing the specific trends in the data, the likely candidate for many collectible items, including basketball cards, is the exponential model. Card values can grow rapidly with increases in popularity or collector interest, often reflecting an exponential growth pattern.
Thus, the best fitting model for basketball card values over time is likely:
an exponential model.