Precalculus Examples

$p = 9000 (1 - \frac{5}{5 + e^{- 0.003 x}})$ , $x = 800$

Step 1

Replace all occurrences of $x$ in $p = 9000 (1 - \frac{5}{5 + e^{- 0.003 x}})$ with $800$ .

$p = 9000 (1 - \frac{5}{5 + e^{- 0.003 \cdot 800}})$

$x = 800$

Step 2

Simplify the right side.

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Step 2.1

Simplify $9000 (1 - \frac{5}{5 + e^{- 0.003 \cdot 800}})$ .

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Step 2.1.1

Simplify terms.

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Step 2.1.1.1

Simplify each term.

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Step 2.1.1.1.1

Simplify the denominator.

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Step 2.1.1.1.1.1

Multiply $- 0.003$ by $800$ .

$p = 9000 (1 - \frac{5}{5 + e^{- 2.4}})$

$x = 800$

Step 2.1.1.1.1.2

Rewrite the expression using the negative exponent rule $b^{- n} = \frac{1}{b^{n}}$ .

$p = 9000 (1 - \frac{5}{5 + \frac{1}{e^{2.4}}})$

$x = 800$

Step 2.1.1.1.1.3

To write $5$ as a fraction with a common denominator, multiply by $\frac{e^{2.4}}{e^{2.4}}$ .

$p = 9000 (1 - \frac{5}{5 \cdot \frac{e^{2.4}}{e^{2.4}} + \frac{1}{e^{2.4}}})$

$x = 800$

Step 2.1.1.1.1.4

Combine $5$ and $\frac{e^{2.4}}{e^{2.4}}$ .

$p = 9000 (1 - \frac{5}{\frac{5 e^{2.4}}{e^{2.4}} + \frac{1}{e^{2.4}}})$

$x = 800$

Step 2.1.1.1.1.5

Combine the numerators over the common denominator.

$p = 9000 (1 - \frac{5}{\frac{5 e^{2.4} + 1}{e^{2.4}}})$

$x = 800$

$p = 9000 (1 - \frac{5}{\frac{5 e^{2.4} + 1}{e^{2.4}}})$

$x = 800$

Step 2.1.1.1.2

Multiply the numerator by the reciprocal of the denominator.

$p = 9000 (1 - (5 (\frac{e^{2.4}}{5 e^{2.4} + 1})))$

$x = 800$

Step 2.1.1.1.3

Combine $5$ and $\frac{e^{2.4}}{5 e^{2.4} + 1}$ .

$p = 9000 (1 - \frac{5 e^{2.4}}{5 e^{2.4} + 1})$

$x = 800$

$p = 9000 (1 - \frac{5 e^{2.4}}{5 e^{2.4} + 1})$

$x = 800$

Step 2.1.1.2

Simplify the expression.

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Step 2.1.1.2.1

Write $1$ as a fraction with a common denominator.

$p = 9000 (\frac{5 e^{2.4} + 1}{5 e^{2.4} + 1} - \frac{5 e^{2.4}}{5 e^{2.4} + 1})$

$x = 800$

Step 2.1.1.2.2

Combine the numerators over the common denominator.

$p = 9000 (\frac{5 e^{2.4} + 1 - 5 e^{2.4}}{5 e^{2.4} + 1})$

$x = 800$

$p = 9000 (\frac{5 e^{2.4} + 1 - 5 e^{2.4}}{5 e^{2.4} + 1})$

$x = 800$

$p = 9000 (\frac{5 e^{2.4} + 1 - 5 e^{2.4}}{5 e^{2.4} + 1})$

$x = 800$

Step 2.1.2

Simplify the numerator.

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Step 2.1.2.1

Subtract $5 e^{2.4}$ from $5 e^{2.4}$ .

$p = 9000 (\frac{0 + 1}{5 e^{2.4} + 1})$

$x = 800$

Step 2.1.2.2

Add $0$ and $1$ .

$p = 9000 (\frac{1}{5 e^{2.4} + 1})$

$x = 800$

$p = 9000 (\frac{1}{5 e^{2.4} + 1})$

$x = 800$

Step 2.1.3

Combine $9000$ and $\frac{1}{5 e^{2.4} + 1}$ .

$p = \frac{9000}{5 e^{2.4} + 1}$

$x = 800$

$p = \frac{9000}{5 e^{2.4} + 1}$

$x = 800$

$p = \frac{9000}{5 e^{2.4} + 1}$

$x = 800$