Precalculus Examples

$A (20) = 800 e^{- 0.0244 \cdot 20}$

Step 1

Simplify.

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Step 1.1

Multiply $- 0.0244$ by $20$ .

$A (20) = 800 e^{- 0.488}$

Step 1.2

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

$A (20) = 800 \frac{1}{e^{0.488}}$

Step 1.3

Combine $800$ and $\frac{1}{e^{0.488}}$ .

$A (20) = \frac{800}{e^{0.488}}$

Step 2

Divide each term in $A (20) = \frac{800}{e^{0.488}}$ by $20$ and simplify.

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Step 2.1

Divide each term in $A (20) = \frac{800}{e^{0.488}}$ by $20$ .

$\frac{A (20)}{20} = \frac{\frac{800}{e^{0.488}}}{20}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $20$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{A \cdot 20}{20} = \frac{\frac{800}{e^{0.488}}}{20}$

Step 2.2.1.2

Divide $A$ by $1$ .

$A = \frac{\frac{800}{e^{0.488}}}{20}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Multiply the numerator by the reciprocal of the denominator.

$A = \frac{800}{e^{0.488}} \cdot \frac{1}{20}$

Step 2.3.2

Combine.

$A = \frac{800 \cdot 1}{e^{0.488} \cdot 20}$

Step 2.3.3

Cancel the common factor of $800$ and $20$ .

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Step 2.3.3.1

Factor $20$ out of $800 \cdot 1$ .

$A = \frac{20 (40 \cdot 1)}{e^{0.488} \cdot 20}$

Step 2.3.3.2

Cancel the common factors.

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Step 2.3.3.2.1

Factor $20$ out of $e^{0.488} \cdot 20$ .

$A = \frac{20 (40 \cdot 1)}{20 \cdot e^{0.488}}$

Step 2.3.3.2.2

Cancel the common factor.

$A = \frac{20 (40 \cdot 1)}{20 \cdot e^{0.488}}$

Step 2.3.3.2.3

Rewrite the expression.

$A = \frac{40 \cdot 1}{e^{0.488}}$

Step 2.3.4

Multiply $40$ by $1$ .

$A = \frac{40}{e^{0.488}}$

Step 3

The result can be shown in multiple forms.

Exact Form:

$A = \frac{40}{e^{0.488}}$

Decimal Form:

$A = 24.55411492 \dots$