The data in the preceding graph represents the value of basketball cards over time. Each point represents the value of a basketball card after a certain number of years. For example, (9,50)

represents a 9-year-old basketball card that is worth $50. Which model best fits this data?

(1 point)
Responses

no model
no model

a quadratic model
a quadratic model

an exponential model
an exponential model

a linear model

1 answer

To determine which model best fits the data represented by the points (where each point corresponds to the value of a basketball card over time), we need to consider the characteristics of each model.

  • Linear Model: A linear model would imply that the card's value increases or decreases by a constant amount each year. This would be represented as a straight line on a graph.

  • Quadratic Model: A quadratic model would suggest that the value of the card changes at an increasing or decreasing rate, which would result in a parabolic shape on the graph.

  • Exponential Model: An exponential model would indicate that the value of the card increases or decreases by a percentage of its current value each year, leading to a curve that grows (or decays) rapidly over time.

Given your description, you would need to assess how the values change as the years increase:

  1. If the values appear to change uniformly over time, a linear model might fit.
  2. If there are signs of increasing or decreasing acceleration in the values, a quadratic model might be appropriate.
  3. If the values seem to grow or shrink rapidly, an exponential model could be the best fit.

Without seeing the actual graph or data points, it's challenging to provide a definitive answer. However, if the basketball card values are increasing rapidly or at a varying rate, then an exponential model might be the best fit. If you notice a steady increase, then a linear model could be appropriate. If the increase in values accelerates, then a quadratic model might be the most suitable choice.

Please review the data or the graph again based on these descriptions to see which model aligns best with the observed trends.