Question

The problem above shows some values for the

function f. If f(x)=ka to the x power for some

constants k and a, what is the value of a?

Answer 1

x= -1,0,1.
f(x)=1/8,1/2,2

Answer 2

tips?

Answer 3

f(x) = ka to the x power,
so \[f(x) = \left( ka \right)^{x}\]
or \[f(x)=ka ^{x}\]

you just need to substitute the value of x into the function, then you'll have three equations, solve the equation to find k and a

Answer 4

k

Answer 5

ahh

Answer 6

1/4 equal a when k=1/32?

Answer 7

opps

Answer 8

a=4 when k=1/8?

Answer 9

that's the correct answer in the book

Answer 10

but why?

Answer 11

are you sure that it's the result?
the given informations are f(-1) = 1/8 ; f(0)=1/2 ; f(1) = 2, right?

Answer 12

wait

Answer 13

don't you just plug in values for f(x)=ka to the x power?

Answer 14

1/8=k4 to the negative one power

Answer 15

1/8=1/4k

Answer 16

k=1/2

Answer 17

1/8=1/2 times 1/4

Answer 18

right?

Answer 19

are did I do it incorrectly?

Answer 20

where do you get 1/8 = k4 and 1/8 = 1/4k ?

Answer 21

let me try out a simpler equatio

Answer 22

2=k4 to the first power

Answer 23

2=4k

Answer 24

1/2=k

Answer 25

2=1/2 times 4=2

Answer 26

\[f(x)= ka ^{x}\]
\[f(-1)=\frac{ 1 }{ 8 }\]
\[ka^{-1}=\frac{1}{8}\]
\[frac{k}{8}=\frac{1}{8}\]

Answer 27

wah?

Answer 28

I thought i Just had to plug in values for the equation f(x)=ka to the x power?

Answer 29

doesn't f(x) equal y?

Answer 30

*the last row
\[\frac{ k }{ a }=\frac{ 1 }{8 }\]

Answer 31

why doesn't 2= k(4 to the first power) work?

Answer 32

yes, f(x) equal to y
you want to find a right?

Answer 33

yeah....

Answer 34

2=4k

Answer 35

1/2=k, right?

Answer 36

yes, k = 1/2
but I get it by using the second information
f(0) = 1/2, so
k x a^0 = 1/2
k = 1/2

Answer 37

hmm

Answer 38

ahh

Answer 39

do

Answer 40

so

Answer 41

1/2=ax to the 0 power

Answer 42

1/2=a

Answer 43

k to the 0 power

Answer 44

the answer is D

Answer 45

4

Answer 46

not 1/2...

Answer 47

wait a sec...

Answer 48

1/2=ka to the 0 power

Answer 49

1/2=k

Answer 50

1/2=1/2a to the x power...

Answer 51

yes, then plug in the value of k into the first equation you have, k/a = 1/8 , then you'll get a

Answer 52

you can do that?

Answer 53

could you do 1/2=1/2(4 to the 0 power)

Answer 54

could you do that?

Answer 55

I got k=1/2

Answer 56

tips?

Answer 57

if you use that equation, any value of a will satisfy the equation since a^0 = 1, so, you cannot use that equation to find a..,

yes, k = 1/2, then to find a , plug in k = 1/2 into k/a = 1/8

Answer 58

where did you get a, though?

Answer 59

where did you get the 1/8?

Answer 60

you have f(-1) = 1/8
so, k x a^(-1) = 1/8
k/a = 1/8

Answer 61

so a=4?

Answer 62

I think I understand your reasoning now

Answer 63

ty

Answer 64

yes

Answer 65

next problem?