Precalculus Examples

$y = 1700 {(1.5)}^{\frac{x}{8}}$

Step 1

Write $y = 1700 {(1.5)}^{\frac{x}{8}}$ as a function.

$f (x) = 1700 {(1.5)}^{\frac{x}{8}}$

Step 2

Consider the difference quotient formula.

$\frac{f (x + h) - f (x)}{h}$

Step 3

Find the components of the definition.

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Step 3.1

Evaluate the function at $x = x + h$ .

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Step 3.1.1

Replace the variable $x$ with $x + h$ in the expression.

$f (x + h) = 1700 {(1.5)}^{\frac{x + h}{8}}$

Step 3.1.2

Simplify the result.

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Step 3.1.2.1

Remove parentheses.

$f (x + h) = 1700 \cdot {1.5}^{\frac{x + h}{8}}$

Step 3.1.2.2

The final answer is $1700 \cdot {1.5}^{\frac{x + h}{8}}$ .

$1700 \cdot {1.5}^{\frac{x + h}{8}}$

Step 3.2

Find the components of the definition.

$f (x + h) = 1700 \cdot {1.5}^{\frac{x + h}{8}}$

$f (x) = 1700 \cdot {1.5}^{\frac{x}{8}}$

$f (x + h) = 1700 \cdot {1.5}^{\frac{x + h}{8}}$

$f (x) = 1700 \cdot {1.5}^{\frac{x}{8}}$

Step 4

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{1700 \cdot {1.5}^{\frac{x + h}{8}} - (1700 \cdot {1.5}^{\frac{x}{8}})}{h}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 1$ by $1700$ .

$\frac{1700 \cdot {1.5}^{\frac{x + h}{8}} - 1700 \cdot {1.5}^{\frac{x}{8}}}{h}$

Step 5.2

Factor $1700$ out of $1700 \cdot {1.5}^{\frac{x + h}{8}} - 1700 \cdot {1.5}^{\frac{x}{8}}$ .

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Step 5.2.1

Factor $1700$ out of $1700 \cdot {1.5}^{\frac{x + h}{8}}$ .

$\frac{1700 \cdot {1.5}^{\frac{x + h}{8}} - 1700 \cdot {1.5}^{\frac{x}{8}}}{h}$

Step 5.2.2

Factor $1700$ out of $- 1700 \cdot {1.5}^{\frac{x}{8}}$ .

$\frac{1700 \cdot {1.5}^{\frac{x + h}{8}} + 1700 (- {1.5}^{\frac{x}{8}})}{h}$

Step 5.2.3

Factor $1700$ out of $1700 \cdot {1.5}^{\frac{x + h}{8}} + 1700 (- {1.5}^{\frac{x}{8}})$ .

$\frac{1700 ({1.5}^{\frac{x + h}{8}} - {1.5}^{\frac{x}{8}})}{h}$

Step 6