Precalculus Examples

$y = 1200 \cdot {(1 + 0.3)}^{t}$

Step 1

Write $y = 1200 \cdot {(1 + 0.3)}^{t}$ as a function.

$f (t) = 1200 \cdot {(1 + 0.3)}^{t}$

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.

$f (t + h) = 1200 \cdot {(1 + 0.3)}^{t + h}$

Step 3.1.2

Simplify the result.

Tap for more steps...

Step 3.1.2.1

Add $1$ and $0.3$ .

$f (t + h) = 1200 \cdot {1.3}^{t + h}$

Step 3.1.2.2

The final answer is $1200 \cdot {1.3}^{t + h}$ .

$1200 \cdot {1.3}^{t + h}$

Step 3.2

Find the components of the definition.

$f (t + h) = 1200 \cdot {1.3}^{t + h}$

$f (t) = 1200 \cdot {1.3}^{t}$

$f (t + h) = 1200 \cdot {1.3}^{t + h}$

$f (t) = 1200 \cdot {1.3}^{t}$

Step 4

Plug in the components.

$\frac{f (t + h) - f t}{h} = \frac{1200 \cdot {1.3}^{t + h} - (1200 \cdot {1.3}^{t})}{h}$

Step 5

Simplify the numerator.

Tap for more steps...

Step 5.1

Multiply $- 1$ by $1200$ .

$\frac{1200 \cdot {1.3}^{t + h} - 1200 \cdot {1.3}^{t}}{h}$

Step 5.2

Factor $1200$ out of $1200 \cdot {1.3}^{t + h} - 1200 \cdot {1.3}^{t}$ .

Tap for more steps...

Step 5.2.1

Factor $1200$ out of $1200 \cdot {1.3}^{t + h}$ .

$\frac{1200 \cdot {1.3}^{t + h} - 1200 \cdot {1.3}^{t}}{h}$

Step 5.2.2

Factor $1200$ out of $- 1200 \cdot {1.3}^{t}$ .

$\frac{1200 \cdot {1.3}^{t + h} + 1200 (- {1.3}^{t})}{h}$

Step 5.2.3

Factor $1200$ out of $1200 \cdot {1.3}^{t + h} + 1200 (- {1.3}^{t})$ .

$\frac{1200 ({1.3}^{t + h} - {1.3}^{t})}{h}$

Step 6