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Chapter 3: Problem 66

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

Short Answer

Expert verified
A scatter plot that suggests modeling the data with an exponential function would show a pattern where the increase or decrease in y values is not linear, but exponential. The data points would form a curve that either rises steeply and then levels off (for exponential growth) or starts high and then drops to level off (for exponential decay).

Step by step solution

01

Understanding Exponential Function

An exponential function can be in the form of \(y = ab^x\), where \(a\) is not equal to zero, \(b\) is greater than zero and not equal to one, and \(x\) is any real number. The base, \(b\), is constant and the exponent, \(x\), is the variable.
02

Visualizing Exponential Growth on Scatter Plot

A scatter plot suggesting modeling the data with an exponential growth function starts from a relatively small y value, if x is near to zero or negative, and as \(x\) increases, \(y\) increases at an ever faster rate. Therefore, the points in the scatter plot would appear to start relatively level and then curve upwards in an increasing exponential fashion.
03

Visualizing Exponential Decay on Scatter Plot

If the scatter plot is suggesting modeling the data with an exponential decay function, it would look like a mirror reflection of the exponential growth scatter plot on y-axis. The points would start off high when \(x\) values are small or negative, and as \(x\) increases, the y values would decrease but at a slower pace, resulting in a curve that steeply falls then levels out.

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