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Twenty-two points are plotted on a scatterplot titled Basketball Card Values. The x-axis is labeled Years, and the y-axis is labeled Dollars.

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 linear model
a linear model

an exponential model
an exponential model

a quadratic model
a quadratic model
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1 answer

To determine which model best fits the scatterplot data of basketball card values over time, we generally analyze the overall trend in the data points.

  1. Linear Model: This model fits if the data points form a roughly straight line. A linear trend would indicate that the value of the basketball cards increases or decreases at a constant rate over the years.

  2. Exponential Model: This model fits if the data points suggest that the value increases (or decreases) at an increasing rate over time. This would typically appear as a curve that steepens as time goes on.

  3. Quadratic Model: This model fits if the data points form a parabolic shape. It indicates that the rate of change itself is changing but not necessarily exponentially.

Without seeing the scatterplot itself, I can't definitively say which model fits best. However, you should look for:

  • If the data points generally form a straight line, select "a linear model."
  • If the value increases more dramatically over time (suggesting compounding growth), select "an exponential model."
  • If the data creates a U-shape or inverted U-shape, select "a quadratic model."

Based on your description, my guess would be that if the values rise sharply as the years increase, you might lean towards "an exponential model." If they rise steadily at a consistent rate, consider "a linear model." If the trend starts to bend, "a quadratic model" may be appropriate.

Please analyze the shape and trend of the scatterplot points accordingly.