Precalculus Examples

$y = 10 {(1 + 0.4)}^{5}$

Step 1

Write $y = 10 {(1 + 0.4)}^{5}$ as a function.

$f (x) = 10 {(1 + 0.4)}^{5}$

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.

$f (x + h) = 10 {(1 + 0.4)}^{5}$

Step 3.1.2

Simplify the result.

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Step 3.1.2.1

Add $1$ and $0.4$ .

$f (x + h) = 10 \cdot {1.4}^{5}$

Step 3.1.2.2

Raise $1.4$ to the power of $5$ .

$f (x + h) = 10 \cdot 5.37824$

Step 3.1.2.3

Multiply $10$ by $5.37824$ .

$f (x + h) = 53.7824$

Step 3.1.2.4

The final answer is $53.7824$ .

$53.7824$

Step 3.2

Find the components of the definition.

$f (x + h) = 53.7824$

$f (x) = 53.7824$

$f (x + h) = 53.7824$

$f (x) = 53.7824$

Step 4

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{53.7824 - (53.7824)}{h}$

Step 5

Simplify.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Multiply $- 1$ by $53.7824$ .

$\frac{53.7824 - 53.7824}{h}$

Step 5.1.2

Subtract $53.7824$ from $53.7824$ .

$\frac{0}{h}$

Step 5.2

Divide $0$ by $h$ .

$0$

Step 6