Algebra Examples

$f (x) = 2 {(\frac{1}{5})}^{x - 5}$

Step 1

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

$y = 2 {(\frac{1}{5})}^{(- 2) - 5}$

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

$y = 2 {(\frac{1}{5})}^{- 2 - 5}$

Step 2.2

Remove parentheses.

$y = 2 {(\frac{1}{5})}^{(- 2) - 5}$

Step 2.3

Simplify $2 {(\frac{1}{5})}^{(- 2) - 5}$ .

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Step 2.3.1

Subtract $5$ from $- 2$ .

$y = 2 {(\frac{1}{5})}^{- 7}$

Step 2.3.2

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

$y = 2 \cdot 5^{7}$

Step 2.3.3

Raise $5$ to the power of $7$ .

$y = 2 \cdot 78125$

Step 2.3.4

Multiply $2$ by $78125$ .

$y = 156250$

Step 3

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

$y = 2 {(\frac{1}{5})}^{(- 1) - 5}$

Step 4

Solve the equation for $y$ .

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Step 4.1

Remove parentheses.

$y = 2 {(\frac{1}{5})}^{- 1 - 5}$

Step 4.2

Remove parentheses.

$y = 2 {(\frac{1}{5})}^{(- 1) - 5}$

Step 4.3

Simplify $2 {(\frac{1}{5})}^{(- 1) - 5}$ .

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Step 4.3.1

Subtract $5$ from $- 1$ .

$y = 2 {(\frac{1}{5})}^{- 6}$

Step 4.3.2

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

$y = 2 \cdot 5^{6}$

Step 4.3.3

Raise $5$ to the power of $6$ .

$y = 2 \cdot 15625$

Step 4.3.4

Multiply $2$ by $15625$ .

$y = 31250$

Step 5

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

$y = 2 {(\frac{1}{5})}^{(0) - 5}$

Step 6

Solve the equation for $y$ .

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Step 6.1

Remove parentheses.

$y = 2 {(\frac{1}{5})}^{0 - 5}$

Step 6.2

Remove parentheses.

$y = 2 {(\frac{1}{5})}^{(0) - 5}$

Step 6.3

Simplify $2 {(\frac{1}{5})}^{(0) - 5}$ .

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Step 6.3.1

Subtract $5$ from $0$ .

$y = 2 {(\frac{1}{5})}^{- 5}$

Step 6.3.2

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

$y = 2 \cdot 5^{5}$

Step 6.3.3

Raise $5$ to the power of $5$ .

$y = 2 \cdot 3125$

Step 6.3.4

Multiply $2$ by $3125$ .

$y = 6250$

Step 7

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

$y = 2 {(\frac{1}{5})}^{(1) - 5}$

Step 8

Solve the equation for $y$ .

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Step 8.1

Remove parentheses.

$y = 2 {(\frac{1}{5})}^{1 - 5}$

Step 8.2

Remove parentheses.

$y = 2 {(\frac{1}{5})}^{(1) - 5}$

Step 8.3

Simplify $2 {(\frac{1}{5})}^{(1) - 5}$ .

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Step 8.3.1

Subtract $5$ from $1$ .

$y = 2 {(\frac{1}{5})}^{- 4}$

Step 8.3.2

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

$y = 2 \cdot 5^{4}$

Step 8.3.3

Raise $5$ to the power of $4$ .

$y = 2 \cdot 625$

Step 8.3.4

Multiply $2$ by $625$ .

$y = 1250$

Step 9

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

$y = 2 {(\frac{1}{5})}^{(2) - 5}$

Step 10

Solve the equation for $y$ .

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Step 10.1

Remove parentheses.

$y = 2 {(\frac{1}{5})}^{2 - 5}$

Step 10.2

Remove parentheses.

$y = 2 {(\frac{1}{5})}^{(2) - 5}$

Step 10.3

Simplify $2 {(\frac{1}{5})}^{(2) - 5}$ .

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Step 10.3.1

Subtract $5$ from $2$ .

$y = 2 {(\frac{1}{5})}^{- 3}$

Step 10.3.2

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

$y = 2 \cdot 5^{3}$

Step 10.3.3

Raise $5$ to the power of $3$ .

$y = 2 \cdot 125$

Step 10.3.4

Multiply $2$ by $125$ .

$y = 250$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & 156250 \\ - 1 & 31250 \\ 0 & 6250 \\ 1 & 1250 \\ 2 & 250 \end{array}$

Step 12