Precalculus Examples

$y = 1700 e^{- 0.074 x}$

Step 1

Write $y = 1700 e^{- 0.074 x}$ as a function.

$f (x) = 1700 e^{- 0.074 x}$

Step 2

Consider the difference quotient formula.

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

Step 3

Find the components of the definition.

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Step 3.1

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

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Step 3.1.1

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

$f (x + h) = 1700 e^{- 0.074 (x + h)}$

Step 3.1.2

Simplify the result.

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Step 3.1.2.1

Apply the distributive property.

$f (x + h) = 1700 e^{- 0.074 x - 0.074 h}$

Step 3.1.2.2

The final answer is $1700 e^{- 0.074 x - 0.074 h}$ .

$1700 e^{- 0.074 x - 0.074 h}$

Step 3.2

Find the components of the definition.

$f (x + h) = 1700 e^{- 0.074 x - 0.074 h}$

$f (x) = 1700 e^{- 0.074 x}$

$f (x + h) = 1700 e^{- 0.074 x - 0.074 h}$

$f (x) = 1700 e^{- 0.074 x}$

Step 4

Plug in the components.

$\frac{f (x + h) - f (x)}{h} = \frac{1700 e^{- 0.074 x - 0.074 h} - (1700 e^{- 0.074 x})}{h}$

Step 5

Simplify the numerator.

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Step 5.1

Multiply $- 1$ by $1700$ .

$\frac{1700 e^{- 0.074 x - 0.074 h} - 1700 e^{- 0.074 x}}{h}$

Step 5.2

Factor $1700$ out of $1700 e^{- 0.074 x - 0.074 h} - 1700 e^{- 0.074 x}$ .

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Step 5.2.1

Factor $1700$ out of $1700 e^{- 0.074 x - 0.074 h}$ .

$\frac{1700 e^{- 0.074 x - 0.074 h} - 1700 e^{- 0.074 x}}{h}$

Step 5.2.2

Factor $1700$ out of $- 1700 e^{- 0.074 x}$ .

$\frac{1700 e^{- 0.074 x - 0.074 h} + 1700 (- e^{- 0.074 x})}{h}$

Step 5.2.3

Factor $1700$ out of $1700 e^{- 0.074 x - 0.074 h} + 1700 (- e^{- 0.074 x})$ .

$\frac{1700 (e^{- 0.074 x - 0.074 h} - e^{- 0.074 x})}{h}$

Step 6