Graph Using a Table of Values y=2(4)^x

$y = 2 {(4)}^{x}$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$y = 2 {(4)}^{- 2}$

Step 2

Solve the equation for $y$ .

Remove parentheses.

$y = 2 \cdot 4^{- 2}$

Remove parentheses.

$y = 2 {(4)}^{- 2}$

Simplify $2 {(4)}^{- 2}$ .

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$y = 2 \frac{1}{4^{2}}$

Raise $4$ to the power of $2$ .

$y = 2 (\frac{1}{16})$

Cancel the common factor of $2$ .

Factor $2$ out of $16$ .

$y = 2 \frac{1}{2 (8)}$

Cancel the common factor.

$y = 2 \frac{1}{2 \cdot 8}$

Rewrite the expression.

$y = \frac{1}{8}$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$y = 2 {(4)}^{- 1}$

Step 4

Solve the equation for $y$ .

Remove parentheses.

$y = 2 \cdot 4^{- 1}$

Remove parentheses.

$y = 2 {(4)}^{- 1}$

Simplify $2 {(4)}^{- 1}$ .

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$y = 2 (\frac{1}{4})$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

$y = 2 \frac{1}{2 (2)}$

Cancel the common factor.

$y = 2 \frac{1}{2 \cdot 2}$

Rewrite the expression.

$y = \frac{1}{2}$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$y = 2 {(4)}^{0}$

Step 6

Solve the equation for $y$ .

Remove parentheses.

$y = 2 \cdot 4^{0}$

Remove parentheses.

$y = 2 {(4)}^{0}$

Simplify $2 {(4)}^{0}$ .

Anything raised to $0$ is $1$ .

$y = 2 \cdot 1$

Multiply $2$ by $1$ .

$y = 2$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$y = 2 {(4)}^{1}$

Step 8

Solve the equation for $y$ .

Remove parentheses.

$y = 2 \cdot 4$

Remove parentheses.

$y = 2 (4)$

Multiply $2$ by $4$ .

$y = 8$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$y = 2 {(4)}^{2}$

Step 10

Solve the equation for $y$ .

Remove parentheses.

$y = 2 \cdot 4^{2}$

Remove parentheses.

$y = 2 {(4)}^{2}$

Simplify $2 {(4)}^{2}$ .

Raise $4$ to the power of $2$ .

$y = 2 \cdot 16$

Multiply $2$ by $16$ .

$y = 32$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & \frac{1}{8} \\ - 1 & \frac{1}{2} \\ 0 & 2 \\ 1 & 8 \\ 2 & 32 \end{array}$

Step 12

Graph Using a Table of Values y=2(4)^x

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