How to find the average rate of change in functions?

Question

anonymous · Answer

Average rate of change of a function between two points is the secant through the two points.

anonymous · Answer

its delta y over delta x

anonymous · Answer

So, my two points are (10, 16.13) and (3, 13.12) I do..$$\frac{ 16.13 }{ 10 }?$$

jdoe0001 · Answer

sorry I was a bit caught up on the other.... the average between two point is the speeds divided by the points in it

anonymous · Answer

This is still the other one, I just tried to break it down into something smaller so I could just do it myself.

jdoe0001 · Answer

(10, 16.13) and (3, 13.12)    <----- does that mean

the rate is 13.12 at point 3 and
16.13 at point 10?

jdoe0001 · Answer

ohh yes, I see is the same =)

anonymous · Answer

Well, thats just a graphed point on the function $$f(n) = 12(1.03)^n$$

jdoe0001 · Answer

ok   so   $\large {  f(n)=12(1.03)^n\quad 
\begin{cases}
n=3\
n=10
\end{cases}
\ \quad \
\cfrac{f(10)-f(3)}{10-3}  }$

anonymous · Answer

And I solve that?

anonymous · Answer

yeah, its delta y over delta x. 
How much y changes as a ratio to the change in x. The order doesn't matter. (you can do f(3)-f(10)/3-10 too)

anonymous · Answer

what does delta mean?? /.\

jdoe0001 · Answer

$\Large \Delta$  is just a notational way to say   " the difference between endpoint and start point values"

anonymous · Answer

Oh..?

jdoe0001 · Answer

site is a bit laggy.... thus

jdoe0001 · Answer

but anyhow... for your case the endpoint value is f(10)   and the start value is f(3)
their difference is f(10) - f(3)

and you divide that by however many points are in between, in this case wil be 7, because 10 - 3

anonymous · Answer

So.. $$\frac{ f(7) }{ 7 }?$$

anonymous · Answer

nono, you need to evaluate f(10)-f(3) then divide by 7.

anonymous · Answer

How do you do that..?

anonymous · Answer

evaluate f(10) then evaluate f(3) (do this by typing it into your calculator) then subtract the two values. THEN divide by 7.

anonymous · Answer

$$f(10) = 12(1.03)^{10} = 16.12699655$$
$$f(3) = 12(1.03)^{3} = 13.112714$$

$$16.12699655 - 13.112714 = 3.01428255$$

$$\frac{ 3.01428255 }{ 7 } = 0.430611793$$

jdoe0001 · Answer

yeap

anonymous · Answer

That's my answer? 0.0

jdoe0001 · Answer

yeap    that's correct