Question

Identify the sequence graphed below and the average rate of change from n = 1 to n = 3.

coordinate plane showing the point 1, 8, point 2, 4, point 4, 1, and point 5, .5

an = 8(one half)n − 1; average rate of change is −3
an = 10(one half)n − 1; average rate of change is 3
an = 8(one half)n − 1; average rate of change is 3
an = 10(one half)n − 1; average rate of change is −3

Answer 1

the x-coordinate is the number of the term, the y-coordinate is the term itself

Answer 2

Btw i think its D

Answer 3

are you sure?

Answer 4

sure that it is D?

Answer 5

I thought it was either A or D...Not 100% sure though

Answer 6

\(\large\color{black}{ \displaystyle a_n=(a_1)\times {\rm r}^{n-1} }\)

Answer 7

Im quite sure its A now...

Answer 8

the common ratio is 1/2 (you can see that every next y-coordinate
is twice smaller than the previous one)

and the first term is 8 (that is given explicitly by the first point)


\(\large\color{black}{ \displaystyle a_n~~=~~(a_1)~~\times ~~{\rm r}~~^{n-1} }\)


\(\large\color{black}{ \displaystyle a_n~~=~~~~8~~~~~\times ~~{\rm \frac{1}{2}}~~^{n-1} }\)

Answer 9

yes, A is better:)

Answer 10

you can tell the rate is negative (because it is an exponential decay)
and you know the first term is 8

Answer 11

and now know that r=1/2

Answer 12

That makes sense :D
I actually graphed it using graphing technology!

Answer 13

Mind checking 2 more for me sire?

Answer 14

sure, cool.....
and the function you are dealing with comes out to be

\(\large\color{black}{ \displaystyle y~~=8\times{\rm \left(\frac{1}{2}\right)}^{x-1} }\)

\(\large\color{black}{ \displaystyle y~~=8\times{\rm \left(\frac{1}{2}\right)}^{x}\times \left(\frac{1}{2}\right)^{-1} }\)

\(\large\color{black}{ \displaystyle y~~=8\times{\rm \left(\frac{1}{2}\right)}^{x}\times \left(2\right) }\)

\(\large\color{black}{ \displaystyle y~~=16{\rm \left(\frac{1}{2}\right)}^{x}}\)

Answer 15

this is just the function in terms of x.... I can check it, but I had a request to help with precalc, when I am done I will do my best to come back

Answer 16

Oh that makes sense...