Question

The graph of f(x) = 2^x + 1 is shown below. Explain how to find the average rate of change between x = 0 and x = 2.

Answer 1

@hartnn can you help? I have no idea how to do this, there is also a graph im going to post that went with the question

Answer 2

know the formula? :)

Answer 3

or does this need to be done using graph only?

Answer 4

um no.... and I actually want to work it out fully not just the answer... cause I know some people just give it, which is nice but I dont get how it works then....

Answer 5

ummm I am not sure about the graph part....

Answer 6

It can be done using a simple formula (similar to slope):
\(\Large \dfrac{f(b)-f(a)}{b-a}\)

here, f(x) = 2^x +1
a= 0
b =2

Answer 7

ok give me a second to work that out

Answer 8

so first get f(0) and f(2)

either from graph or by plugging in

Answer 9

um what do you mean by that? just plug them in, and actually I have no idea what to do.....

Answer 10

f(x) = 2^x + 1

to get f(0) , just replace 'x' by '0'

f(0) = 2^0 + 1 = ..?

Answer 11

ohhhhh ok one minute

Answer 12

2 to the 0 power would just be 2 correct? I have never done a 0 power before, and in that case

f(0)=3

Answer 13

(anything except 0)^0 = 1

Answer 14

oh f(0)=1 not 3

Answer 15

f(0)= 2^0+1=1+1=

Answer 16

2?

Answer 17

yes f(0)=2

how about f(2)=..?

Answer 18

f(2)=5 I believe

Answer 19

yesss, just plug these values in the formula i gave

Answer 20

\[\frac{ 5-2 }{ 2-0 }=\frac{ 3 }{ -2 }\]

or would the -2 make the whole thing negative?

Answer 21

ignore that for a minute....

Answer 22

so looking back at it I think I messed up with that, it should be \[\frac{ 3 }{ 3 }\] correct?

Answer 23

5-2 = 3
2-0 = 2

so, the rate of change is 3/2 :)

Answer 24

ohh ok, sorry I was good the first time, I originally thought the bottom ones were switched to f(b) and f(a) sorry had an idiot moment... but thanks for you help :D

Answer 25

welcome ^_^

do you know how to find slope of line give 2 points?

Answer 26

I believe you need to use slope-intercept form correct?

or a formula like x1-x2/y1-y2..... its been a while since I did slope actually...

Answer 27

yes,
the formula is
\(\huge m=\frac{y_1-y_2}{x_1-x_2}\)


Just wanted to let you know the 2 independent ways of doing this same problem/

1. The formula way, which we did here. Only using f(x).

2. The graph way:
>> Find the y values from graph for the 2 x values given.
So, you'll get y = 2 for x = 0, y = 5 for x= 2
so, your 2 points are (0,2),(2,5)
Find the slope of line containing these 2 points,
and you'll get the same answer :)

Answer 28

ahh ok, thanks, I am gonna write it down, im studing up cause Im gonna retake the Math PERT test to try getting into college math, and questions like this were common on it :)

Answer 29

cool!
and good luck :)