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Chapter 7: Problem 43

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

Short Answer

Expert verified
The scatter plot suggesting an exponential model will exhibit a pattern where the data points either increase or decrease rapidly. This represents a steep curve either upwards (for an increasing function) or downwards (for a decreasing function). The data either starts high and falls quickly, or starts low and rises quickly as you move along the x-axis.

Step by step solution

01

Identify the Form of an Exponential Function

Recall that an exponential function often takes the form \( f(x) = a\cdot b^{x} \), where \( a \) is not equal to 0, \( b > 0 \) and \( b \) is not equal to 1. This means that the y-values increase or decrease rapidly as the x-values change.
02

Understand Scatter Plots

Scatter plots are graphs that display two variables in a data set, one along the x-axis and one along the y-axis. Each point on the plot represents a single observation from the data set.
03

Relating Scatter Plots and Exponential Functions

In a scatter plot that suggests modeling the data with an exponential function: 1) The pattern of the points should either be increasing or decreasing rapidly. 2) Data that starts high and falls quickly, or starts low and rises quickly, indicates an exponential function. As you move from extreme left to the right, the data increases or decrease drastically.

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