Precalculus Examples

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

Step 1

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

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

Step 2

Consider the difference quotient formula.

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

Step 3

Find the components of the definition.

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Step 3.1

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

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Step 3.1.1

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

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

Step 3.1.2

Simplify the result.

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Step 3.1.2.1

Add $1$ and $0.75$ .

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

Step 3.1.2.2

The final answer is $350 \cdot {1.75}^{t + h}$ .

$350 \cdot {1.75}^{t + h}$

Step 3.2

Find the components of the definition.

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

$f (t) = 350 \cdot {1.75}^{t}$

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

$f (t) = 350 \cdot {1.75}^{t}$

Step 4

Plug in the components.

$\frac{f (t + h) - f t}{h} = \frac{350 \cdot {1.75}^{t + h} - (350 \cdot {1.75}^{t})}{h}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 1$ by $350$ .

$\frac{350 \cdot {1.75}^{t + h} - 350 \cdot {1.75}^{t}}{h}$

Step 5.2

Factor $350$ out of $350 \cdot {1.75}^{t + h} - 350 \cdot {1.75}^{t}$ .

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Step 5.2.1

Factor $350$ out of $350 \cdot {1.75}^{t + h}$ .

$\frac{350 \cdot {1.75}^{t + h} - 350 \cdot {1.75}^{t}}{h}$

Step 5.2.2

Factor $350$ out of $- 350 \cdot {1.75}^{t}$ .

$\frac{350 \cdot {1.75}^{t + h} + 350 (- {1.75}^{t})}{h}$

Step 5.2.3

Factor $350$ out of $350 \cdot {1.75}^{t + h} + 350 (- {1.75}^{t})$ .

$\frac{350 ({1.75}^{t + h} - {1.75}^{t})}{h}$

Step 6