Precalculus Examples

$V (t) = 2 e^{1.4 t} + 35$

Step 1

Consider the difference quotient formula.

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

Step 2

Find the components of the definition.

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Step 2.1

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

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Step 2.1.1

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

$V (t + h) = 2 e^{1.4 (t + h)} + 35$

Step 2.1.2

Simplify the result.

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Step 2.1.2.1

Apply the distributive property.

$V (t + h) = 2 e^{1.4 t + 1.4 h} + 35$

Step 2.1.2.2

The final answer is $2 e^{1.4 t + 1.4 h} + 35$ .

$2 e^{1.4 t + 1.4 h} + 35$

Step 2.2

Find the components of the definition.

$V (t + h) = 2 e^{1.4 t + 1.4 h} + 35$

$V (t) = 2 e^{1.4 t} + 35$

$V (t + h) = 2 e^{1.4 t + 1.4 h} + 35$

$V (t) = 2 e^{1.4 t} + 35$

Step 3

Plug in the components.

$\frac{V (t + h) - V t}{h} = \frac{2 e^{1.4 t + 1.4 h} + 35 - (2 e^{1.4 t} + 35)}{h}$

Step 4

Simplify the numerator.

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Step 4.1

Apply the distributive property.

$\frac{2 e^{1.4 t + 1.4 h} + 35 - (2 e^{1.4 t}) - 1 \cdot 35}{h}$

Step 4.2

Multiply $2$ by $- 1$ .

$\frac{2 e^{1.4 t + 1.4 h} + 35 - 2 e^{1.4 t} - 1 \cdot 35}{h}$

Step 4.3

Multiply $- 1$ by $35$ .

$\frac{2 e^{1.4 t + 1.4 h} + 35 - 2 e^{1.4 t} - 35}{h}$

Step 4.4

Subtract $35$ from $35$ .

$\frac{2 e^{1.4 t + 1.4 h} + 0 - 2 e^{1.4 t}}{h}$

Step 4.5

Add $2 e^{1.4 t + 1.4 h}$ and $0$ .

$\frac{2 e^{1.4 t + 1.4 h} - 2 e^{1.4 t}}{h}$

Step 4.6

Factor $2$ out of $2 e^{1.4 t + 1.4 h} - 2 e^{1.4 t}$ .

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Step 4.6.1

Factor $2$ out of $2 e^{1.4 t + 1.4 h}$ .

$\frac{2 e^{1.4 t + 1.4 h} - 2 e^{1.4 t}}{h}$

Step 4.6.2

Factor $2$ out of $- 2 e^{1.4 t}$ .

$\frac{2 e^{1.4 t + 1.4 h} + 2 (- e^{1.4 t})}{h}$

Step 4.6.3

Factor $2$ out of $2 e^{1.4 t + 1.4 h} + 2 (- e^{1.4 t})$ .

$\frac{2 (e^{1.4 t + 1.4 h} - e^{1.4 t})}{h}$

Step 5