Question

What is the average rate of change of the function f(n) from n = 2 to n = 6, and what does it represent?
f(n) = 8(1.05)^n

Answer 1

@TheSmartOne

Answer 2

@.Sam.

Answer 3

@ParthKohli

Answer 4

@imqwerty

Answer 5

alright so \[ f(n) = 8(1.05)^{n}\]

Answer 6

yes

Answer 7

so what this seems like to me is like we start off with a number 8 right and it's growing by 5%

Answer 8

we can probably find the slope of this.

HINT; rate of change is

\[m = \frac{ \Delta~y }{ \Delta~x } = \frac{ y_{2}-y_{1} }{ x_{2}-x_{1} }\]

so can you first find the y value when n = 2

\[8(1.05)^{2} = ?\]


and n = 6

\[8(1.05)^{6} = ?\]

Answer 9

honestly all i need to be able to find out is the average rate of change

Answer 10

we are doing that..and i'm tying to show you how to do that.

Answer 11

ok

Answer 12

so I was asking if you could figure out what

8(1.05)^2 = ?

and

8(1.05)^6

Answer 13

8.82 and 10.72

Answer 14

alright so now let's put this together

n = 2, f(2) = 8.82
n = 6, f(6) = 10.72

\[\frac{ f(6)-f(2) }{ n_{2}-n_{1} } = m\]

Answer 15

tell me what you get

Answer 16

@PeriodicNinja

Answer 17

-5.04? @Photon336

Answer 18

how did you get that answer?

Answer 19

was i supposed to keep the 6 and 2 inside of f(x)

Answer 20

Here's how you set it up

\[\frac{ (10.72)-(0.82) }{ (6-2) } = ?\]

Answer 21

i put it upside down

Answer 22

@PeriodicNinja do you see how I did it?

Answer 23

yeah

Answer 24

take a look. at the graph I'll post it.

if we take the slope that we just found right and then make a line in which we put that in for example a line that goes through (2,8.82) we get this

Answer 25

typo above that should be 8.82

Answer 26

http://prntscr.com/bn6v8s

Answer 27

here the slope is 0.475 or the average rate of change between n = 2 and n = 6

Answer 28

but like any graph, I believe this is exponential, the graph will get steeper as you increase in x.