Precalculus Examples

$\frac{10000}{5 + 1245 e^{- 0.97 \cdot 5}}$

Step 1

Cancel the common factor of $10000$ and $5 + 1245 e^{- 0.97 \cdot 5}$ .

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Step 1.1

Factor $5$ out of $10000$ .

$\frac{5 \cdot 2000}{5 + 1245 e^{- 0.97 \cdot 5}}$

Step 1.2

Cancel the common factors.

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Step 1.2.1

Factor $5$ out of $5$ .

$\frac{5 \cdot 2000}{5 (1) + 1245 e^{- 0.97 \cdot 5}}$

Step 1.2.2

Factor $5$ out of $1245 e^{- 0.97 \cdot 5}$ .

$\frac{5 \cdot 2000}{5 (1) + 5 (249 e^{- 0.97 \cdot 5})}$

Step 1.2.3

Factor $5$ out of $5 (1) + 5 (249 e^{- 0.97 \cdot 5})$ .

$\frac{5 \cdot 2000}{5 (1 + 249 e^{- 0.97 \cdot 5})}$

Step 1.2.4

Cancel the common factor.

$\frac{5 \cdot 2000}{5 (1 + 249 e^{- 0.97 \cdot 5})}$

Step 1.2.5

Rewrite the expression.

$\frac{2000}{1 + 249 e^{- 0.97 \cdot 5}}$

Step 2

Simplify the denominator.

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Step 2.1

Multiply $- 0.97$ by $5$ .

$\frac{2000}{1 + 249 e^{- 4.85}}$

Step 2.2

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

$\frac{2000}{1 + 249 \frac{1}{e^{4.85}}}$

Step 2.3

Combine $249$ and $\frac{1}{e^{4.85}}$ .

$\frac{2000}{1 + \frac{249}{e^{4.85}}}$

Step 2.4

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

$\frac{2000}{\frac{e^{4.85}}{e^{4.85}} + \frac{249}{e^{4.85}}}$

Step 2.5

Combine the numerators over the common denominator.

$\frac{2000}{\frac{e^{4.85} + 249}{e^{4.85}}}$

Step 3

Multiply the numerator by the reciprocal of the denominator.

$2000 \frac{e^{4.85}}{e^{4.85} + 249}$

Step 4

Combine $2000$ and $\frac{e^{4.85}}{e^{4.85} + 249}$ .

$\frac{2000 e^{4.85}}{e^{4.85} + 249}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{2000 e^{4.85}}{e^{4.85} + 249}$

Decimal Form:

$678.13482859 \dots$