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Chapter 7: Problem 44

Describe the shape of a scatter plot that suggests modeling the data with a logarithmic function.

Short Answer

Expert verified
A scatter plot suggesting a logarithmic function would show a high density of points on one end which spreads out or 'levels off' as it extends along the x-axis. The points should start off being very closely grouped, then begin to scatter and flatten as they move away from the origin.

Step by step solution

01

Understand the Characteristics of a Logarithmic Function

Recognize that logarithmic functions exhibit a specific shape characterized by a sharp increase or decrease at the beginning, followed by a leveling off as you move along the x-axis. In a scatter plot, points start off being very close together then begin to spread out and flatten as it moves away from the y-axis.
02

Identify the Shape within the Scatter Plot

Look for a scatter plot that displays a closely compacted group of points on one end, indicating high density, followed by a gradual reduction of point density spread out along the remaining part of the x-axis. The points should not be evenly spaced out in the plot.
03

Considering the Characteristics

Comparing the characteristics of a logarithmic function to the scatter plot, if the plot satisfies the criteria outlined in step 1 and 2, it is feasible to suggest that the data represented by the scatter plot may be modeled using a logarithmic function.

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