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A Deeper Look at Exponential Functions

This graph is a residual plot displaying the residuals for the bacteria growth when a linear regression equation is applied to the data.  The horizontal axis represents the time (in minutes) and extends from negative 1 to 25.  The vertical axis represents the residual values and extends from negative 1.7 to 2.  The graph displays the following ordered pairs:  (0, 1.429), (5, negative 0.543), (10, negative 0.514), (15, negative 1.486), (20, negative 0.457), and (25, 1.571).

The correlation coefficient is 0.994, which indicates a strong correlation.  However, the residual plot indicates that while the residuals are small, there may be a pattern to the data.

So, it will be important to also check exponential functions.  In the context of the problem, an exponential model may make sense, as population data is typically exponential in nature.

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