Precalculus Examples

$p (4 \frac{1}{2}) = 900 e^{0.04 (4 \frac{1}{2})}$

Step 1

Simplify the left side.

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Step 1.1

Simplify $p (4 \frac{1}{2})$ .

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Step 1.1.1

Convert $4 \frac{1}{2}$ to an improper fraction.

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Step 1.1.1.1

A mixed number is an addition of its whole and fractional parts.

$p (4 + \frac{1}{2}) = 900 e^{0.04 (4 \frac{1}{2})}$

Step 1.1.1.2

Add $4$ and $\frac{1}{2}$ .

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Step 1.1.1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$p (4 \cdot \frac{2}{2} + \frac{1}{2}) = 900 e^{0.04 (4 \frac{1}{2})}$

Step 1.1.1.2.2

Combine $4$ and $\frac{2}{2}$ .

$p (\frac{4 \cdot 2}{2} + \frac{1}{2}) = 900 e^{0.04 (4 \frac{1}{2})}$

Step 1.1.1.2.3

Combine the numerators over the common denominator.

$p \frac{4 \cdot 2 + 1}{2} = 900 e^{0.04 (4 \frac{1}{2})}$

Step 1.1.1.2.4

Simplify the numerator.

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Step 1.1.1.2.4.1

Multiply $4$ by $2$ .

$p \frac{8 + 1}{2} = 900 e^{0.04 (4 \frac{1}{2})}$

Step 1.1.1.2.4.2

Add $8$ and $1$ .

$p \frac{9}{2} = 900 e^{0.04 (4 \frac{1}{2})}$

Step 1.1.2

Combine $p$ and $\frac{9}{2}$ .

$\frac{p \cdot 9}{2} = 900 e^{0.04 (4 \frac{1}{2})}$

Step 1.1.3

Move $9$ to the left of $p$ .

$\frac{9 p}{2} = 900 e^{0.04 (4 \frac{1}{2})}$

Step 2

Simplify the right side.

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Step 2.1

Simplify $900 e^{0.04 (4 \frac{1}{2})}$ .

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Step 2.1.1

Convert $4 \frac{1}{2}$ to an improper fraction.

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Step 2.1.1.1

A mixed number is an addition of its whole and fractional parts.

$\frac{9 p}{2} = 900 e^{0.04 (4 + \frac{1}{2})}$

Step 2.1.1.2

Add $4$ and $\frac{1}{2}$ .

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Step 2.1.1.2.1

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{9 p}{2} = 900 e^{0.04 (4 \cdot \frac{2}{2} + \frac{1}{2})}$

Step 2.1.1.2.2

Combine $4$ and $\frac{2}{2}$ .

$\frac{9 p}{2} = 900 e^{0.04 (\frac{4 \cdot 2}{2} + \frac{1}{2})}$

Step 2.1.1.2.3

Combine the numerators over the common denominator.

$\frac{9 p}{2} = 900 e^{0.04 \frac{4 \cdot 2 + 1}{2}}$

Step 2.1.1.2.4

Simplify the numerator.

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Step 2.1.1.2.4.1

Multiply $4$ by $2$ .

$\frac{9 p}{2} = 900 e^{0.04 \frac{8 + 1}{2}}$

Step 2.1.1.2.4.2

Add $8$ and $1$ .

$\frac{9 p}{2} = 900 e^{0.04 (\frac{9}{2})}$

Step 2.1.2

Cancel the common factor of $0.04$ .

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Step 2.1.2.1

Factor $0.04$ out of $2$ .

$\frac{9 p}{2} = 900 e^{0.04 \frac{9}{0.04 (50)}}$

Step 2.1.2.2

Cancel the common factor.

$\frac{9 p}{2} = 900 e^{0.04 \frac{9}{0.04 \cdot 50}}$

Step 2.1.2.3

Rewrite the expression.

$\frac{9 p}{2} = 900 e^{\frac{9}{50}}$

Step 3

Multiply both sides of the equation by $\frac{2}{9}$ .

$\frac{2}{9} \cdot \frac{9 p}{2} = \frac{2}{9} (900 e^{\frac{9}{50}})$

Step 4

Simplify both sides of the equation.

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Step 4.1

Simplify the left side.

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Step 4.1.1

Simplify $\frac{2}{9} \cdot \frac{9 p}{2}$ .

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Step 4.1.1.1

Cancel the common factor of $2$ .

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Step 4.1.1.1.1

Cancel the common factor.

$\frac{2}{9} \cdot \frac{9 p}{2} = \frac{2}{9} (900 e^{\frac{9}{50}})$

Step 4.1.1.1.2

Rewrite the expression.

$\frac{1}{9} (9 p) = \frac{2}{9} (900 e^{\frac{9}{50}})$

Step 4.1.1.2

Cancel the common factor of $9$ .

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Step 4.1.1.2.1

Factor $9$ out of $9 p$ .

$\frac{1}{9} (9 (p)) = \frac{2}{9} (900 e^{\frac{9}{50}})$

Step 4.1.1.2.2

Cancel the common factor.

$\frac{1}{9} (9 p) = \frac{2}{9} (900 e^{\frac{9}{50}})$

Step 4.1.1.2.3

Rewrite the expression.

$p = \frac{2}{9} (900 e^{\frac{9}{50}})$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{2}{9} (900 e^{\frac{9}{50}})$ .

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Step 4.2.1.1

Cancel the common factor of $9$ .

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Step 4.2.1.1.1

Factor $9$ out of $900 e^{\frac{9}{50}}$ .

$p = \frac{2}{9} (9 (100 e^{\frac{9}{50}}))$

Step 4.2.1.1.2

Cancel the common factor.

$p = \frac{2}{9} (9 (100 e^{\frac{9}{50}}))$

Step 4.2.1.1.3

Rewrite the expression.

$p = 2 (100 e^{\frac{9}{50}})$

Step 4.2.1.2

Multiply $100$ by $2$ .

$p = 200 e^{\frac{9}{50}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$p = 200 e^{\frac{9}{50}}$

Decimal Form:

$p = 239.44347262 \dots$