Question

Complete the tables of values.

Answer 1

for
`f(x) =4^(-x)` the value
`a=1,\ b=(1)/(16),\ c=(1)/(256)`

for
`f(x) =((2)/(3))^(x)` the value
`a=1,\ b=(4)/(9),\ c=(16)/(81)`

Explanation:

Consider

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

We have to find the values at certain given points.

at x = 0

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

at x = 2

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

at x= 4

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

Thus,
`a=1,\ b=(1)/(16),\ c=(1)/(256)`

Consider

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

We have to find the values at certain given points.

at x = 0

`f(x) =((2)/(3))^(0)=1`

at x = 2

`f(x) =((2)/(3))^(2)=((4)/(9))`

at x = 4

`f(x) =((2)/(3))^(4)=(16)/(81)`

Thus,
`a=1,\ b=(4)/(9),\ c=(16)/(81)`

Answer 2

Answer with Step-by-step explanation:

We are given two tables and we are to complete the missing values.

For table one, we are to substitute the given values of x in the term
`4^(-x)`:

when x = 0,
`4^(-0) = 1`

when x = 2,
`4^(-2) = (1)/(16)`

when x = 4,
`4^(-4) = (1)/(256)`

For table two, we are to substitute the given values of x in the term
`((2)/(3) )^x`:

when x = 0,
`((2)/(3) )^0 = 1`

when x = 2,
`((2)/(3) )^2 = (4)/(9)`

when x = 4,
`((2)/(3) )^4 = (16)/(81)`