Question

Completing the table of Values.
Complete the tables of value.

Answer 1

A-1

B-1/16

C-1/256

D-1

E-4/9

F-16/81

Answer 2

Part 1)
`a=1`

Part 2)
`b=1/16`

Part 3)
`c=1/256`

Part 4)
`d=1`

Part 5)
`e=(4)/(9)`

Part 6)
`f=(16)/(81)`

Explanation:

we know that

The function in the orange table is equal to

`f(x)=4^(-x)=1/(4^(x))`

so

step 1

Find the value of a

The value of a is the value of the function f(x) for
`x=0`

Substitute the value of
`x=0` in the function

`f(0)=1/(4^(0))=1`

therefore

`a=1`

step 2

Find the value of b

The value of b is the value of the function f(x) for
`x=2`

Substitute the value of
`x=2` in the function

`f(2)=1/(4^(2))=1/16`

therefore

`b=1/16`

step 3

Find the value of c

The value of a is the value of the function f(x) for
`x=4`

Substitute the value of
`x=4` in the function

`f(4)=1/(4^(4))=1/256`

therefore

`c=1/256`

The function in the blue table is equal to

`g(x)=((2)/(3))^(x)`

so

step 4

Find the value of d

The value of d is the value of the function g(x) for
`x=0`

Substitute the value of
`x=0` in the function

`g(0)=((2)/(3))^(0)=1`

therefore

`d=1`

step 5

Find the value of e

The value of e is the value of the function g(x) for
`x=2`

Substitute the value of
`x=2` in the function

`g(2)=((2)/(3))^(2)=(4)/(9)`

therefore

`e=(4)/(9)`

step 6

Find the value of f

The value of f is the value of the function g(x) for
`x=4`

Substitute the value of
`x=4` in the function

`g(4)=((2)/(3))^(4)=(16)/(81)`

therefore

`f=(16)/(81)`