Algebra Examples

$y = 4 \cdot {(\frac{1}{2})}^{x - 1} - 2$

Step 1

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

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

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

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

Step 2.2

Remove parentheses.

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

Step 2.3

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

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Subtract $1$ from $- 2$ .

$y = 4 \cdot {(\frac{1}{2})}^{- 3} - 2$

Step 2.3.1.2

Change the sign of the exponent by rewriting the base as its reciprocal.

$y = 4 \cdot 2^{3} - 2$

Step 2.3.1.3

Raise $2$ to the power of $3$ .

$y = 4 \cdot 8 - 2$

Step 2.3.1.4

Multiply $4$ by $8$ .

$y = 32 - 2$

Step 2.3.2

Subtract $2$ from $32$ .

$y = 30$

Step 3

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

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

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

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

Step 4.2

Remove parentheses.

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

Step 4.3

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

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Step 4.3.1

Simplify each term.

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Step 4.3.1.1

Subtract $1$ from $- 1$ .

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

Step 4.3.1.2

Change the sign of the exponent by rewriting the base as its reciprocal.

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

Step 4.3.1.3

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

$y = 4 \cdot 4 - 2$

Step 4.3.1.4

Multiply $4$ by $4$ .

$y = 16 - 2$

Step 4.3.2

Subtract $2$ from $16$ .

$y = 14$

Step 5

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

$y = 4 \cdot {(\frac{1}{2})}^{(0) - 1} - 2$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = 4 \cdot {(\frac{1}{2})}^{0 - 1} - 2$

Step 6.2

Remove parentheses.

$y = 4 \cdot {(\frac{1}{2})}^{(0) - 1} - 2$

Step 6.3

Simplify $4 \cdot {(\frac{1}{2})}^{(0) - 1} - 2$ .

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Step 6.3.1

Simplify each term.

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Step 6.3.1.1

Subtract $1$ from $0$ .

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

Step 6.3.1.2

Change the sign of the exponent by rewriting the base as its reciprocal.

$y = 4 \cdot 2 - 2$

Step 6.3.1.3

Multiply $4$ by $2$ .

$y = 8 - 2$

Step 6.3.2

Subtract $2$ from $8$ .

$y = 6$

Step 7

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

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

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

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

Step 8.2

Remove parentheses.

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

Step 8.3

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

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Step 8.3.1

Simplify each term.

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Step 8.3.1.1

Subtract $1$ from $1$ .

$y = 4 \cdot {(\frac{1}{2})}^{0} - 2$

Step 8.3.1.2

Apply the product rule to $\frac{1}{2}$ .

$y = 4 \cdot \frac{1^{0}}{2^{0}} - 2$

Step 8.3.1.3

Anything raised to $0$ is $1$ .

$y = 4 \cdot \frac{1}{2^{0}} - 2$

Step 8.3.1.4

Anything raised to $0$ is $1$ .

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

Step 8.3.1.5

Cancel the common factor of $1$ .

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Step 8.3.1.5.1

Cancel the common factor.

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

Step 8.3.1.5.2

Rewrite the expression.

$y = 4 \cdot 1 - 2$

Step 8.3.1.6

Multiply $4$ by $1$ .

$y = 4 - 2$

Step 8.3.2

Subtract $2$ from $4$ .

$y = 2$

Step 9

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

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

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

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

Step 10.2

Remove parentheses.

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

Step 10.3

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

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Step 10.3.1

Simplify each term.

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Step 10.3.1.1

Subtract $1$ from $2$ .

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

Step 10.3.1.2

Simplify.

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

Step 10.3.1.3

Cancel the common factor of $2$ .

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Step 10.3.1.3.1

Factor $2$ out of $4$ .

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

Step 10.3.1.3.2

Cancel the common factor.

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

Step 10.3.1.3.3

Rewrite the expression.

$y = 2 - 2$

Step 10.3.2

Subtract $2$ from $2$ .

$y = 0$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & 30 \\ - 1 & 14 \\ 0 & 6 \\ 1 & 2 \\ 2 & 0 \end{array}$

Step 12