Question

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

Answer 1

Answer:

Part 1) $a=1$

Part 2) $b=1/16$

Part 3) $c=1/256$

Part 4) $d=1$

Part 5) $e=\frac{4}{9}$

Part 6) $f=\frac{16}{81}$

Step-by-step 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

$g(x)=(\frac{2}{3})^{x}$

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

$g(0)=(\frac{2}{3})^{0}=1$

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

$g(2)=(\frac{2}{3})^{2}=\frac{4}{9}$

therefore

$e=\frac{4}{9}$

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

$g(4)=(\frac{2}{3})^{4}=\frac{16}{81}$

therefore

$f=\frac{16}{81}$