Algebra Examples

$f (x) = \frac{3}{4} {(10)}^{- x}$

Step 1

Write $f (x) = \frac{3}{4} {(10)}^{- x}$ as an equation.

$y = \frac{3}{4} {(10)}^{- x}$

Step 2

Solve the equation for $y$ .

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Step 2.1

Remove parentheses.

$y = \frac{3}{4} \cdot 10^{- x}$

Step 2.2

Combine $\frac{3}{4}$ and $10^{- x}$ .

$y = \frac{3 \cdot 10^{- x}}{4}$

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.

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Step 4.1

Remove parentheses.

$y = \frac{3 \cdot 10^{- (0)}}{4}$

Step 4.2

Simplify $\frac{3 \cdot 10^{- (0)}}{4}$ .

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Step 4.2.1

Simplify the numerator.

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Step 4.2.1.1

Multiply $- 1$ by $0$ .

$y = \frac{3 \cdot 10^{0}}{4}$

Step 4.2.1.2

Anything raised to $0$ is $1$ .

$y = \frac{3 \cdot 1}{4}$

Step 4.2.2

Multiply $3$ by $1$ .

$y = \frac{3}{4}$

Step 4.3

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

$(0, \frac{3}{4})$

Step 5

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

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Step 5.1

Remove parentheses.

$y = \frac{3 \cdot 10^{- (1)}}{4}$

Step 5.2

Simplify $\frac{3 \cdot 10^{- (1)}}{4}$ .

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Step 5.2.1

Move $10^{- (1)}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$y = \frac{3}{4 \cdot 10}$

Step 5.2.2

Multiply $4$ by $10$ .

$y = \frac{3}{40}$

Step 5.3

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

$(1, \frac{3}{40})$

Step 6

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

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Step 6.1

Remove parentheses.

$y = \frac{3 \cdot 10^{- (2)}}{4}$

Step 6.2

Simplify $\frac{3 \cdot 10^{- (2)}}{4}$ .

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Step 6.2.1

Move $10^{- (2)}$ to the denominator using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$y = \frac{3}{4 \cdot 10^{2}}$

Step 6.2.2

Divide using scientific notation.

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Step 6.2.2.1

Group coefficients together and exponents together to divide numbers in scientific notation.

$y = (\frac{3}{4}) (\frac{1}{10^{2}})$

Step 6.2.2.2

Divide $3$ by $4$ .

$y = 0.75 \frac{1}{10^{2}}$

Step 6.2.2.3

Move $10^{2}$ to the numerator using the negative exponent rule $\frac{1}{b^{n}} = b^{- n}$ .

$y = 0.75 \cdot 10^{- 2}$

Step 6.2.3

Move the decimal point in $0.75$ to the right by $1$ place and decrease the power of $10^{- 2}$ by $1$ .

$y = 7.5 \cdot 10^{- 3}$

Step 6.3

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

$(2, 7.5 \cdot 10^{- 3})$

Step 7

These are three possible solutions to the equation.

$(0, \frac{3}{4}), (1, \frac{3}{40}), (2, 7.5 \cdot 10^{- 3})$

Step 8