Question

Which exponential function goes through the points (1, 8) and (4, 64)? f(x) = 4(2)x f(x) = 2(4)x f(x) = 4(2)-x f(x) = 2(4)-x

Answer 1

there

Answer 2

alrighty

Answer 3

:}

Answer 4

An exponential function has a general form of

Y = C*a^x

Answer 5

yes

Answer 6

\[y = C*a^x\]

Answer 7

points given are (1,8) and (4,64) right?

Answer 8

yes

Answer 9

so since we have 2 points, we can form 2 equations from that general form..

\[8 = C*a^1 ~~~~~and~~~~~64 = C*a^4\]

Answer 10

see that?

Answer 11

yes ok, so what should i do next.

Answer 12

now we have 2 equations with 2 unknowns, a and C, we can solve them and figure out a and C!

Answer 13

oops i got excited exclamation. lol

Answer 14

:} ok

Answer 15

Lets take the first equation and solve it for C

\[8 = C*a^1\]

Answer 16

\[C = \frac{ 8 }{ a }\]

Answer 17

you get that part?

Answer 18

alright so far im still with you ;}

Answer 19

ok, since we have C=8/a , lets put that value into the second equation...
\[64 = C*a^4\]

\[64 = \frac{ 8 }{ a }*a^4\]

Answer 20

good with that?

Answer 21

ok

Answer 22

now we solve a right

Answer 23

exactly, what you have so far is
\[64 = 8*\frac{ a^4 }{ a }\]

divide both sides by 8 first

Answer 24

speaking of which i did 8 x 8 because i was trying to plug in my choices, and for my answer i chose A because i was wondering when talking about the ^x i figured i would do what you displayed above.

Answer 25

I see, you could plug into the answers and see what works, but you should learn how to do this... what if no multiple choice is given? .lol we are almost there i promis

so after dividing by 8 on both sides you get
\[8 = \frac{ a^4 }{ a }\]

Answer 26

\[\frac{ a^4 }{ a } = \frac{ a^4*a ^{-1} }{ 1 } = a ^{4-1} = a ^{3}\]

Answer 27

oh i wasnt worried about rushing im in no hurry i was just wondering if that tactic would work but yeah your method works for me as well.

Answer 28

a^3 = 8

the cubed root of 8 is 2..... 2*2*2 = 8

so we figured out that a = 2

Answer 29

you see that part?

Answer 30

yes

Answer 31

i figured that part

Answer 32

now we have 'a'

y = C*a^x

y = C*2^x

we can find out what C is now

Answer 33

What were the original 2 points given?

Answer 34

(1,8) and (4,64)

Answer 35

(1, 8) and (4, 64)

Answer 36

we can use one of those points in the equation, and figure out C

use ( 1 , 8) the power of a^1 is easier than a^4 from the other point

Answer 37

tjhats kind of what i did.

Answer 38

thats*

Answer 39

y = C*2^x point(x,y) = (1,8)

8 = C*2^1

8 = 2C

C = 4

Answer 40

overall equation , now that we found 'a' and C is

\[\large\color{blue}{ y = 4*2^x}\]

Answer 41

yes i solved that too however the putting it all together is what stumbled me. but yeah now i see it.

Answer 42

so was i correct for picking A originally.

Answer 43

if so then im :}

Answer 44

cool, so now anytime you get a question that gives you 2 points and says it is exponential (y=C*a^x) , you can figure out the equation! right?

Answer 45

1) Make an equation using each point
2) solve one equation for C
3) put that C into the second equation
3) Solve that for a =
4) Now you have a, use one point and that 'a' in the y=C*a^x to find C
5) done

Answer 46

Go back through and right out all the steps on paper, it will be clear

Answer 47

done i wrote it

Answer 48

cool, if you want to run through another for practice, ill help out if you want

Answer 49

ok sure i guess i have free time.

Answer 50

k

Answer 51

did you have one in mind or should i pull one up.

Answer 52

up to you :}

Answer 53

@DanJS thanks

Answer 54

change of plan got to go maybe another day? bye and thanks again! :}

Answer 55

@triciaal you are welcome, what are you thanking me for? lol

Answer 56

@DanJS responding when I tagged
patiently helping the "cool kid"
reminding me about the function notation y = c*a^x that the poster meant.