Precalculus Examples

$y = 350 {(1 + 0.75)}^{5}$

Step 1

Write $y = 350 {(1 + 0.75)}^{5}$ as a function.

$f (x) = 350 {(1 + 0.75)}^{5}$

Step 2

Consider the difference quotient formula.

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

Step 3

Find the components of the definition.

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

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

$f (x + h) = 350 {(1 + 0.75)}^{5}$

Step 3.1.2

Simplify the result.

Tap for more steps...

Step 3.1.2.1

Add $1$ and $0.75$ .

$f (x + h) = 350 \cdot {1.75}^{5}$

Step 3.1.2.2

Raise $1.75$ to the power of $5$ .

$f (x + h) = 350 \cdot 16.41308593$

Step 3.1.2.3

Multiply $350$ by $16.41308593$ .

$f (x + h) = 5744.58007812$

Step 3.1.2.4

The final answer is $5744.58007812$ .

$5744.58007812$

Step 3.2

Find the components of the definition.

$f (x + h) = 5744.58007812$

$f (x) = 5744.58007812$

$f (x + h) = 5744.58007812$

$f (x) = 5744.58007812$

Step 4

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{5744.58007812 - (5744.58007812)}{h}$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Simplify the numerator.

Tap for more steps...

Step 5.1.1

Multiply $- 1$ by $5744.58007812$ .

$\frac{5744.58007812 - 5744.58007812}{h}$

Step 5.1.2

Subtract $5744.58007812$ from $5744.58007812$ .

$\frac{0}{h}$

Step 5.2

Divide $0$ by $h$ .

$0$

Step 6