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

$f (x) = 2 {(5)}^{x}$

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

$y = 2 {(5)}^{- 2}$

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

$y = 2 {(5)}^{- 2}$

Simplify $2 {(5)}^{- 2}$ .

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

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

Raise $5$ to the power of $2$ .

$y = 2 (\frac{1}{25})$

Combine $2$ and $\frac{1}{25}$ .

$y = \frac{2}{25}$

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

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

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

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

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

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

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

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

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

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

$y = 2 {(5)}^{0}$

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

$y = 2 {(5)}^{0}$

Simplify $2 {(5)}^{0}$ .

Anything raised to $0$ is $1$ .

$y = 2 \cdot 1$

Multiply $2$ by $1$ .

$y = 2$

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

$y = 2 {(5)}^{1}$

Solve the equation for $y$ .

Remove parentheses.

$y = 2 \cdot 5$

Remove parentheses.

$y = 2 (5)$

Multiply $2$ by $5$ .

$y = 10$

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

$y = 2 {(5)}^{2}$

Solve the equation for $y$ .

Remove parentheses.

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

Remove parentheses.

$y = 2 {(5)}^{2}$

Simplify $2 {(5)}^{2}$ .

Raise $5$ to the power of $2$ .

$y = 2 \cdot 25$

Multiply $2$ by $25$ .

$y = 50$

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

$\begin{array}{c} x & y \\ - 2 & \frac{2}{25} \\ - 1 & \frac{2}{5} \\ 0 & 2 \\ 1 & 10 \\ 2 & 50 \end{array}$

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

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