Precalculus Examples

$30 {(1.05)}^{3}$

Step 1

Write $30 {(1.05)}^{3}$ as a function.

$f (x) = 30 {(1.05)}^{3}$

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.

$f (x + h) = 30 {(1.05)}^{3}$

Step 3.1.2

Simplify the result.

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Step 3.1.2.1

Raise $1.05$ to the power of $3$ .

$f (x + h) = 30 \cdot 1.157625$

Step 3.1.2.2

Multiply $30$ by $1.157625$ .

$f (x + h) = 34.72875$

Step 3.1.2.3

The final answer is $34.72875$ .

$34.72875$

Step 3.2

Find the components of the definition.

$f (x + h) = 34.72875$

$f (x) = 34.72875$

$f (x + h) = 34.72875$

$f (x) = 34.72875$

Step 4

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{34.72875 - (34.72875)}{h}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Multiply $- 1$ by $34.72875$ .

$\frac{34.72875 - 34.72875}{h}$

Step 5.1.2

Subtract $34.72875$ from $34.72875$ .

$\frac{0}{h}$

Step 5.2

Divide $0$ by $h$ .

$0$

Step 6