Question

The sequence an = 1(3)n − 1 is graphed below:

Find the average rate of change between n = 1 and n = 3.

Answer 1

The rate of change is
\[m = \frac{ rise }{run }\]

Answer 2

\(\bf slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}\implies \cfrac{f(3)-f(1)}{3-1}\impliedby \textit{rate of change}\)

Answer 3

i'm confused ): which coordinates am I using?

Answer 4

"rate of change between n = 1 and n = 3. "
^ ^

Answer 5

Would the answer be 3? or 1/3?

Answer 6

well... what's f(3) and f(1) ? or what is \(\bf \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}\) based on the given points or 1 and 3 ?

Answer 7

what is the value of y at n = 3
what is the value of y at n = 1

that is the total change

Answer 8

divide that over the change in n (n = 3, n =1)

Answer 9

\[\frac{ Y2-Y1 }{ X2-X1 } \] in order to do this, don't I need to coordinates? would I take (1,3) and (3,9) ?

Answer 10

yes

Answer 11

\(\bf \begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
&({\color{red}{ 1}}\quad ,&{\color{blue}{ 1}})\quad &({\color{red}{ 3}}\quad ,&{\color{blue}{ 9}})
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= \cfrac{rise}{run} \implies \cfrac{{\color{blue}{ y_2}}-{\color{blue}{ y_1}}}{{\color{red}{ x_2}}-{\color{red}{ x_1}}}\)

Answer 12

4!!!!

Answer 13

Yes!