Precalculus Examples

$y = 55 \cdot {(1 - 0.02)}^{t}$

Step 1

Write $y = 55 \cdot {(1 - 0.02)}^{t}$ as a function.

$f (t) = 55 \cdot {(1 - 0.02)}^{t}$

Step 2

Consider the difference quotient formula.

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

Step 3

Find the components of the definition.

Tap for more steps...

Step 3.1

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

Tap for more steps...

Step 3.1.1

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

$f (t + h) = 55 \cdot {(1 - 0.02)}^{t + h}$

Step 3.1.2

Simplify the result.

Tap for more steps...

Step 3.1.2.1

Subtract $0.02$ from $1$ .

$f (t + h) = 55 \cdot {0.98}^{t + h}$

Step 3.1.2.2

The final answer is $55 \cdot {0.98}^{t + h}$ .

$55 \cdot {0.98}^{t + h}$

Step 3.2

Find the components of the definition.

$f (t + h) = 55 \cdot {0.98}^{t + h}$

$f (t) = 55 \cdot {0.98}^{t}$

$f (t + h) = 55 \cdot {0.98}^{t + h}$

$f (t) = 55 \cdot {0.98}^{t}$

Step 4

Plug in the components.

$\frac{f (t + h) - f t}{h} = \frac{55 \cdot {0.98}^{t + h} - (55 \cdot {0.98}^{t})}{h}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $- 1$ by $55$ .

$\frac{55 \cdot {0.98}^{t + h} - 55 \cdot {0.98}^{t}}{h}$

Step 5.2

Factor $55$ out of $55 \cdot {0.98}^{t + h} - 55 \cdot {0.98}^{t}$ .

Tap for more steps...

Step 5.2.1

Factor $55$ out of $55 \cdot {0.98}^{t + h}$ .

$\frac{55 \cdot {0.98}^{t + h} - 55 \cdot {0.98}^{t}}{h}$

Step 5.2.2

Factor $55$ out of $- 55 \cdot {0.98}^{t}$ .

$\frac{55 \cdot {0.98}^{t + h} + 55 (- {0.98}^{t})}{h}$

Step 5.2.3

Factor $55$ out of $55 \cdot {0.98}^{t + h} + 55 (- {0.98}^{t})$ .

$\frac{55 ({0.98}^{t + h} - {0.98}^{t})}{h}$

Step 6