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Vladimir [108]
4 years ago
15

The sequence an= 27(1/3)^n-1 is graphed below. find the average rate of change between n=2 and n=4

Mathematics
1 answer:
antiseptic1488 [7]4 years ago
6 0
The average rate of change, is pretty much just the "slope" of the graph, therefore since we know that when n = 2, y = 9, notice the point (2,9), and when n = 4, y = 1, notice the point (4,1), thus

\bf \begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
%  (a,b)
&&(~ 2 &,& 9~) 
%  (c,d)
&&(~ 4 &,& 1~)
\end{array}
\\\\\\
% slope  = m
\stackrel{\textit{average rate of change}}{slope} =  m\implies 
\cfrac{\stackrel{rise}{ y_2- y_1}}{\stackrel{run}{ x_2- x_1}}\implies \cfrac{1-9}{4-2}\implies \cfrac{-8}{2}\implies -4
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