Find Three Ordered Pair Solutions f(x)=1/6(2/5)^x

$f (x) = \frac{1}{6} {(\frac{2}{5})}^{x}$

Step 1

Write $f (x) = \frac{1}{6} {(\frac{2}{5})}^{x}$ as an equation.

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

Step 2

Simplify $\frac{1}{6} \cdot {(\frac{2}{5})}^{x}$ .

Apply the product rule to $\frac{2}{5}$ .

$y = \frac{1}{6} \cdot \frac{2^{x}}{5^{x}}$

Combine.

$y = \frac{1 \cdot 2^{x}}{6 \cdot 5^{x}}$

Multiply $2^{x}$ by $1$ .

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

Step 3

Choose any value for $x$ that is in the domain to plug into the equation.

Step 4

Choose $0$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

$y = \frac{2^{0}}{6 \cdot 5^{0}}$

Simplify $\frac{2^{0}}{6 \cdot 5^{0}}$ .

Anything raised to $0$ is $1$ .

$y = \frac{1}{6 \cdot 5^{0}}$

Anything raised to $0$ is $1$ .

$y = \frac{1}{6 \cdot 1}$

Multiply $6$ by $1$ .

$y = \frac{1}{6}$

Use the $x$ and $y$ values to form the ordered pair.

$(0, \frac{1}{6})$

Step 5

Choose $1$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

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

Simplify $\frac{2}{6 \cdot 5}$ .

Cancel the common factor of $2$ and $6$ .

Factor $2$ out of $2$ .

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

Cancel the common factors.

Factor $2$ out of $6 \cdot 5$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = \frac{1}{3 \cdot 5}$

Multiply $3$ by $5$ .

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

Use the $x$ and $y$ values to form the ordered pair.

$(1, \frac{1}{15})$

Step 6

Choose $2$ to substitute in for $x$ to find the ordered pair.

Remove parentheses.

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

Simplify $\frac{2^{2}}{6 \cdot 5^{2}}$ .

Simplify the expression.

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

$y = \frac{4}{6 \cdot 5^{2}}$

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

$y = \frac{4}{6 \cdot 25}$

Multiply $6$ by $25$ .

$y = \frac{4}{150}$

Cancel the common factor of $4$ and $150$ .

Factor $2$ out of $4$ .

$y = \frac{2 (2)}{150}$

Cancel the common factors.

Factor $2$ out of $150$ .

$y = \frac{2 \cdot 2}{2 \cdot 75}$

Cancel the common factor.

$y = \frac{2 \cdot 2}{2 \cdot 75}$

Rewrite the expression.

$y = \frac{2}{75}$

Use the $x$ and $y$ values to form the ordered pair.

$(2, \frac{2}{75})$

Step 7

These are three possible solutions to the equation.

$(0, \frac{1}{6}), (1, \frac{1}{15}), (2, \frac{2}{75})$

Step 8

Find Three Ordered Pair Solutions f(x)=1/6(2/5)^x

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