Question

What is the average rate of change of the function f(x)=2(3)x from x = 2 to x = 4?

Answer 1

is the problem \(f(x)=2(3)^x\)?

Answer 2

Yes

Answer 3

next time, i suggest you write the problem as f(x) = 2(3)^x instead
^ denotes exponents

when x=2 what is 2(3)^x =?

when x=4 what is 2(3)^x=?

Answer 4

It would be \[f4=2(3)^{4}\], right?

Answer 5

f(4)
yes

Answer 6

Just f(4)?

Answer 7

f(4) = 2(3)^4
the parenthesis is important

now, when you punch the right side into a calculator, what value do you get?

Answer 8

\[f(4)=2(3)^{4}\]?

Answer 9

3^4 = 81
2*81 = ?

Answer 10

162

Answer 11

right, so when x=4, then f(4) =162

Answer 12

so when x=2, f(2) = ?

Answer 13

Ok, so should I just write 162 or actually write f(4)=162?

Answer 14

write f(4)=162, though thats not the answer

Answer 15

Okay so one question, how did we get 81?

Answer 16

oh, im guessing you're not familiar with powers

if you have x*x*x*x*x

its not fun to write out 5 x's
so instead you represent it as
\(x^5\)

Answer 17

Oh right, 3x3x3x3

Answer 18

so 3^4=\(=3^4=3*3*3*3=9*9=81\)

Answer 19

Okay understood now :)

Answer 20

ok, so the 2nd step,
what is f(2)=?
or f(x) when x=2?

Answer 21

So when 2 is X 2=4

Answer 22

2x2=4

Answer 23

why?
the function f(x) = 2(3)^x

what happened to the 3?

Answer 24

all you're doing is just replacing the x with 2

Answer 25

Oh

Answer 26

So 2 would either be f(2) or (3)^2

Answer 27

no...

when you substitute 2 in, you get

f(2) = 2(3)^2

cant separate/ignore the equal sign

Answer 28

f(2) = 2(3)^2
so what does
2(3)^2 =?

Answer 29

9?

Answer 30

3^2 = 9
so 2(3^2) = 2*9 = ?

Answer 31

18

Answer 32

ok so f(2) = 18

yes?

Answer 33

i mean ify ou want to show your steps, which teachers love looking at, you can write it
f(2) =2(3)^2 = 18

or just break it up into 2 steps

Answer 34

So 18 is the answer?

Answer 35

f(2) = 2(3)^2
f(2)=18

Answer 36

And yea I would like to do that

Answer 37

no...

what is your question asking? copy and paste it

Answer 38

What is the average rate of change of the function f(x)=2(3)x from x = 2 to x = 4?

Answer 39

??

Answer 40

ok, average rate of change

it is the equivalent of saying , what is the slope?

Answer 41

between the two points x =2 and x=4

Answer 42

Isn't it 3?

Answer 43

That was wrong, wasn't it?

Answer 44

What is the avergae rate of change then?

Answer 45

Cuz I'm just lost

Answer 46

sorry, forgot i was still doing this

do you remember what slope is? or what hte slope formula is ?

Answer 47

Slope is something is basically the term that happens evently, like how many gallons he/she used per mile. Sorry I'm not exactly a good explainer

Answer 48

or miles per gallon, this is a rate, similar to rate of change being asked in your problem

but more generally, slope ona graph describes how steep the curve is

Answer 49

Oh

Answer 50

now, if you have 2 points, then if you remember the slope formula,
\[m=\frac{y_2 - y_1}{x_2-x_1}\]

Answer 51

except this case, we have no y

actually, you can consider f(x) as y

so f(2) = y2 and f(4) = y1, x2= 2 and x1 =4

Answer 52

substitute that all in and tell me what m would be

m is slope

Answer 53

oh uhh...

Answer 54

I'm sorry for giving a hard time, I'm not very sure

Answer 55

My mind is just so stupid when it comes to equation formulas

Answer 56

ok, that the information you already have , put it in terms of ordered pairs

f(4) = 162 :: (4,162)
f(2)= 18 :: ( 2, 18)

Answer 57

Ahh okay, that makes sence

Answer 58

does that make it a bit more clear?

now, apply these points to the slope formula \[ m= \frac{y_1-y_2}{x_1-x_2}\]

Answer 59

the resulting value would be the slope aka rate of change

Answer 60

But how would I apply these numbers to the slope formula?

Answer 61

ordered pairs come in the form
(x,y)

Answer 62

always

Answer 63

Is the answer 9?

Answer 64

I divided 162 by 18, and I just thought that it might be a way to solve it

Answer 65

doesnt matter which order you do the subtraction, as long as its in the same order top and bottom

that sounds a bit low

\[\frac{162-18}{4-2}\]

Answer 66

\[\frac{ 162-18 }{4-2}=\frac{18-162}{2-4}\]

Answer 67

So do I subtract those?

Answer 68

162- 18 =?

Answer 69

144

Answer 70

4-2=?

Answer 71

2

Answer 72

144/2=?

Answer 73

72

Answer 74

m= 72

now you understand how to find slope from 2 points?

Answer 75

or rate of change between 2 point?

Answer 76

Oh, lol math is such a Jerk XD and yes

Answer 77

math has an specific order in which to do things, this order is unchanging,

as long as you understand the order, things really are not that hard

though i do suggest you memorize the slope formula or basic theory on how you find slope from 2 points, you will probablly see it alot in the future, so better to learn it now rather than having to constantly relearn it over and over and over and over again

Answer 78

Okay, I've taken notes from this discussion

Answer 79

also, if you;re familiar with PEMDAS or BODMAS or BEDMAS

fractions if you want to write it linearly are written [numerator]/[denominator]

Answer 80

Bodmas and Bedmas? Never heard of those

Answer 81

writing x1-x2/y1-y2 = \(x_1 -\frac{x2}{y1} -y2\)

Answer 82

in canada i think its Bedmas- bracket exponent etc.

Answer 83

Oh okay

Answer 84

some places call it bracket , order, and switch multiplicatio nadn division

Answer 85

all the same thing though, "order of operations"

Answer 86

lol I'll remember that

Answer 87

well, good luck with the rest

Answer 88

Thx so much, you were such a great help

Answer 89

and a study tip,

while this website is still up, try to help people with their problem and explain how to get the answer (since last i heard its closing next year)

try to understand the concept well enough that you are able to explain it other, a bit like reviewing the concept and they might ask you questions you mightve never thought of when initially learning

Answer 90

Will do, but I have to go right now