Graph Using a Table of Values f(x)=15(6/5)^x

$f (x) = 15 {(\frac{6}{5})}^{x}$

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

$y = 15 {(\frac{6}{5})}^{- 2}$

Solve the equation for $y$ .

Remove parentheses.

$y = 15 {(\frac{6}{5})}^{- 2}$

Simplify $15 {(\frac{6}{5})}^{- 2}$ .

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

$y = 15 {(\frac{5}{6})}^{2}$

Simplify the expression.

Apply the product rule to $\frac{5}{6}$ .

$y = 15 \frac{5^{2}}{6^{2}}$

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

$y = 15 \frac{25}{6^{2}}$

Raise $6$ to the power of $2$ .

$y = 15 (\frac{25}{36})$

Cancel the common factor of $3$ .

Factor $3$ out of $15$ .

$y = 3 (5) \frac{25}{36}$

Factor $3$ out of $36$ .

$y = 3 \cdot 5 \frac{25}{3 \cdot 12}$

Cancel the common factor.

$y = 3 \cdot 5 \frac{25}{3 \cdot 12}$

Rewrite the expression.

$y = 5 (\frac{25}{12})$

Combine $5$ and $\frac{25}{12}$ .

$y = \frac{5 \cdot 25}{12}$

Multiply $5$ by $25$ .

$y = \frac{125}{12}$

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

$y = 15 {(\frac{6}{5})}^{- 1}$

Solve the equation for $y$ .

Remove parentheses.

$y = 15 {(\frac{6}{5})}^{- 1}$

Simplify $15 {(\frac{6}{5})}^{- 1}$ .

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

$y = 15 (\frac{5}{6})$

Cancel the common factor of $3$ .

Factor $3$ out of $15$ .

$y = 3 (5) \frac{5}{6}$

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Multiply $5$ by $5$ .

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

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

$y = 15 {(\frac{6}{5})}^{0}$

Solve the equation for $y$ .

Remove parentheses.

$y = 15 {(\frac{6}{5})}^{0}$

Simplify $15 {(\frac{6}{5})}^{0}$ .

Simplify the expression.

Apply the product rule to $\frac{6}{5}$ .

$y = 15 \frac{6^{0}}{5^{0}}$

Anything raised to $0$ is $1$ .

$y = 15 \frac{1}{5^{0}}$

Anything raised to $0$ is $1$ .

$y = 15 (\frac{1}{1})$

Cancel the common factor of $1$ .

Cancel the common factor.

$y = 15 (\frac{1}{1})$

Rewrite the expression.

$y = 15 \cdot 1$

Multiply $15$ by $1$ .

$y = 15$

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

$y = 15 {(\frac{6}{5})}^{1}$

Solve the equation for $y$ .

Remove parentheses.

$y = 15 (\frac{6}{5})$

Simplify $15 (\frac{6}{5})$ .

Cancel the common factor of $5$ .

Factor $5$ out of $15$ .

$y = 5 (3) \frac{6}{5}$

Cancel the common factor.

$y = 5 \cdot 3 \frac{6}{5}$

Rewrite the expression.

$y = 3 \cdot 6$

Multiply $3$ by $6$ .

$y = 18$

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

$y = 15 {(\frac{6}{5})}^{2}$

Solve the equation for $y$ .

Remove parentheses.

$y = 15 {(\frac{6}{5})}^{2}$

Simplify $15 {(\frac{6}{5})}^{2}$ .

Simplify the expression.

Apply the product rule to $\frac{6}{5}$ .

$y = 15 \frac{6^{2}}{5^{2}}$

Raise $6$ to the power of $2$ .

$y = 15 \frac{36}{5^{2}}$

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

$y = 15 (\frac{36}{25})$

Cancel the common factor of $5$ .

Factor $5$ out of $15$ .

$y = 5 (3) \frac{36}{25}$

Factor $5$ out of $25$ .

$y = 5 \cdot 3 \frac{36}{5 \cdot 5}$

Cancel the common factor.

$y = 5 \cdot 3 \frac{36}{5 \cdot 5}$

Rewrite the expression.

$y = 3 (\frac{36}{5})$

Combine $3$ and $\frac{36}{5}$ .

$y = \frac{3 \cdot 36}{5}$

Multiply $3$ by $36$ .

$y = \frac{108}{5}$

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

$\begin{array}{c} x & y \\ - 2 & \frac{125}{12} \\ - 1 & \frac{25}{2} \\ 0 & 15 \\ 1 & 18 \\ 2 & \frac{108}{5} \end{array}$

Graph Using a Table of Values f(x)=15(6/5)^x

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