Finite Math Examples

$5 = x {(1 + \frac{0.051}{365})}^{365 \cdot \frac{216}{12}}$

Step 1

Rewrite the equation as $x {(1 + \frac{0.051}{365})}^{365 \cdot \frac{216}{12}} = 5$ .

$x {(1 + \frac{0.051}{365})}^{365 \cdot \frac{216}{12}} = 5$

Step 2

Simplify.

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Step 2.1

Divide $216$ by $12$ .

$x {(1 + \frac{0.051}{365})}^{365 \cdot 18} = 5$

Step 2.2

Multiply $365$ by $18$ .

$x {(1 + \frac{0.051}{365})}^{6570} = 5$

Step 2.3

Divide $0.051$ by $365$ .

$x {(1 + 0.00013972)}^{6570} = 5$

Step 2.4

Add $1$ and $0.00013972$ .

$x \cdot {1.00013972}^{6570} = 5$

Step 3

Divide each term in $x \cdot {1.00013972}^{6570} = 5$ by ${1.00013972}^{6570}$ and simplify.

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Step 3.1

Divide each term in $x \cdot {1.00013972}^{6570} = 5$ by ${1.00013972}^{6570}$ .

$\frac{x \cdot {1.00013972}^{6570}}{{1.00013972}^{6570}} = \frac{5}{{1.00013972}^{6570}}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of ${1.00013972}^{6570}$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{x \cdot {1.00013972}^{6570}}{{1.00013972}^{6570}} = \frac{5}{{1.00013972}^{6570}}$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{5}{{1.00013972}^{6570}}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Raise $1.00013972$ to the power of $6570$ .

$x = \frac{5}{2.50411623}$

Step 3.3.2

Divide $5$ by $2.50411623$ .

$x = 1.99671242$