You can use the given function to evaluate the expected sales at year 2009 and 2015 and use the net difference divided by time as the average rate of change.
The average rate of change in expected sales from 2009 to 2015 is given by $12,059,941
How to find the average rate of change of something?
Let the thing that is changing be y and the thing with which the rate is being compared is x, then we have the average rate of change of y as x changes as:
[tex]\text{Average rate} = \dfrac{y_2 - y_1}{x_2 - x_1}[/tex]
where when
[tex]x = x_1, y = y_1\\and \\x = x_2, y = y_2[/tex]
Using the above method to calculate the needed average rate
Since the sales is given by the function [tex]g(t) = t^3 - 2t^2 + 4t - 7[/tex], and the inputs are 2009 and 2015, thus, evaluating g(t) (sales) at those values of t, we get:
[tex]g(2009) = 8023737057[/tex] (replaced 2009 with t and calculated)
[tex]g(2015) = 8096096703[/tex] (replaced 2015 with t and calculated)
Using these values to calculate the average rate
[tex]\text{average rate} = \dfrac{g(2015) - g(2009)}{2015 - 2009} = \dfrac{72359646}{6} = 12059941\\[/tex]
Thus,
The average rate of change in expected sales from 2009 to 2015 is given by $12,059,941
Learn more about rate of change here:
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