Graph Using a Table of Values f(x)=5*(1/2)^x

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

Step 1

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

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

Step 2

Solve the equation for $y$ .

Remove parentheses.

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

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

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

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

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

$y = 5 \cdot 4$

Multiply $5$ by $4$ .

$y = 20$

Step 3

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

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

Step 4

Solve the equation for $y$ .

Remove parentheses.

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

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

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

$y = 5 \cdot 2$

Multiply $5$ by $2$ .

$y = 10$

Step 5

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

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

Step 6

Solve the equation for $y$ .

Remove parentheses.

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

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

Simplify the expression.

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

$y = 5 \cdot \frac{1^{0}}{2^{0}}$

Anything raised to $0$ is $1$ .

$y = 5 \cdot \frac{1}{2^{0}}$

Anything raised to $0$ is $1$ .

$y = 5 \cdot \frac{1}{1}$

Cancel the common factor of $1$ .

Cancel the common factor.

$y = 5 \cdot \frac{1}{1}$

Rewrite the expression.

$y = 5 \cdot 1$

Multiply $5$ by $1$ .

$y = 5$

Step 7

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

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

Step 8

Solve the equation for $y$ .

Remove parentheses.

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

Combine $5$ and $\frac{1}{2}$ .

$y = \frac{5}{2}$

Step 9

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

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

Step 10

Solve the equation for $y$ .

Remove parentheses.

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

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

Simplify the expression.

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

$y = 5 \cdot \frac{1^{2}}{2^{2}}$

One to any power is one.

$y = 5 \cdot \frac{1}{2^{2}}$

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

$y = 5 \cdot \frac{1}{4}$

Combine $5$ and $\frac{1}{4}$ .

$y = \frac{5}{4}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & 20 \\ - 1 & 10 \\ 0 & 5 \\ 1 & \frac{5}{2} \\ 2 & \frac{5}{4} \end{array}$

Step 12

Graph Using a Table of Values f(x)=5*(1/2)^x

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