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Sagot :
Part A)
The average rate of change of the sales S(t) between two times t₁ and t₂ is given by:
[tex]\frac{S(t_2)-S(t_1)}{t_2-t_1}_{}[/tex]Between the years 2012 and 2015, the average rate of change is:
[tex]\frac{S(2015)-S(2012)}{2015-2012}[/tex]Notice that S(2015) = 107.1 and S(2012)=61.09. Then, the average rate of change in net sales per year, is:
[tex]\frac{107.01-61.09}{3}=15.30666\ldots[/tex]The numerator is measured in billions of dollars and the denominator is measured in years. Then, the units of measure are billions of dollars per year.
Part B)
Assuming that the trend continues, the average rate of change must be the same for S(2018).
Replace S(2018) and S(2015) as well as 2018 and 2015 into the formula, set it equal to 15.30666... and solve for S(2018) to find the estimated net sales for 2018:
[tex]\begin{gathered} \frac{S(2018)-S(2015)}{2018-2015}=15.30666\ldots \\ \Rightarrow\frac{S(2018)-107.01}{3}=15.30666\ldots \\ \Rightarrow S(2018)-107.01=3\times15.30666\ldots \\ \Rightarrow S(2018)=3\times15.30666\ldots+107.01 \\ \therefore S(2018)=152.93 \end{gathered}[/tex]Therefore, the answers are:
a) The average rate of change in net sales from 2012 to 2015 is 15.30666... billions of dollars per year.
b) The estimated net sales for the year 2018 if this trend continues is 152.93 billions of dollars.
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