Question

The table contains some points on the graph of an exponential function.

Capture.PNG"

Determine the a and b values and formulate a model exponential equation to represent the data in the table. Based on the table, which value of a and b and which function represent the same relationship?

Answer 1

someone pls help me.....

Answer 2

i dont know anything.........

Answer 3

I'm assuming you also have answer choices?

Regardless,
exponential functions are in the form of

\(y = ab^x\)

we have to plug in the values given to us in the table to figure out what a and b are

Answer 4

so the first point, we have

x = 0 and y = 6

plug it in

\( 6 = ab^{0}\)

Answer 5

do you know what anything to the power of 0 is?

Answer 6

i think so

Answer 7

anything to the power of 0 is 1

so what is b^ 0 =

Answer 8

B^1?

Answer 9

what is b^0 =

I just told you that anything to the power of 0 equals 1

so 10^0 = 1
a^0 = 1

what is b^0 =

Answer 10

it's not a trick question

Answer 11

=1

Answer 12

Good!

\(\color{#0cbb34}{\text{Originally Posted by}}\) @AZ
so the first point, we have

x = 0 and y = 6

plug it in

\( 6 = ab^{0}\)
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 13

So now we have

6 = a * 1

what is a equal to?

Answer 14

would it be 6 bc its multiplying by 1?

Answer 15

yes!

so now that we know a, let's solve for b

so we have

\(\Large y = 6b^x\)

Answer 16

Let's plug in the next point (1, 9)

x = 1
and y = 9

\(\Large 9 = 6 \times (\text{b}^1)\)

what is b^1 =

Answer 17

anything to the power of 1 is the same thing

so like

13^1 = 13

Answer 18

so its 1

Answer 19

no...

Answer 20

what is b to the power of 1

b^1 =

anything to the power of 1 is that same thing

ex. d^1 = d

Answer 21

oh ...B

Answer 22

yes so now we have

9 = 6 * b

what is b = ?

Answer 23

......6

Answer 24

what number times 6 will give you 9

Answer 25

b times six equals 9

b * 6 = 9

we want to move six to the other side
divide it on both sides then

Answer 26

well 6 divied by 9 is 0.66

Answer 27

no

Answer 28

or 1.5

Answer 29

look let me change the letter because b is looking a whole lot like 6

let's make it F

F * 6 = 9

Answer 30

if we're dividing 6 on both sides

Answer 31

do you do 6/ 9

or 9/ 6

???????????????

Answer 32

we want to get the letter all by itself
so we divide by 6 on both sides

Answer 33

well 9 divied by 6 is 1.5

Answer 34

there you go

Answer 35

so that's the value of b

Answer 36

now what's the final correct answer?

we said a was 6
and b was 1.5

\(\Large y = ab^x\)

Answer 37

y=6a(1.5b)\[y=6a1.5b ^{x}\]

Answer 38

no, you get rid of the a and the b and put the numbers instead

do you see your answer choices having an `a` and `b` ????????????

Answer 39

6(1.5)x

Answer 40

there you go

(I know you copy pasted but otherwise it should be (1.5)^x )

Answer 41

so the answer choice is B

Answer 42

yes

Answer 43

thank you!

Answer 44

you're welcome!