Calculus Examples

$50000 (10) + 12000000 (10) e^{- 0.05 \cdot 10} + 24000000 e^{- 0.05 \cdot 10}$

Step 1

Simplify each term.

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Step 1.1

Multiply $50000$ by $10$ .

$500000 + 12000000 (10) e^{- 0.05 \cdot 10} + 24000000 e^{- 0.05 \cdot 10}$

Step 1.2

Multiply $12000000$ by $10$ .

$500000 + 120000000 e^{- 0.05 \cdot 10} + 24000000 e^{- 0.05 \cdot 10}$

Step 1.3

Multiply $- 0.05$ by $10$ .

$500000 + 120000000 e^{- 0.5} + 24000000 e^{- 0.05 \cdot 10}$

Step 1.4

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

$500000 + 120000000 \frac{1}{e^{0.5}} + 24000000 e^{- 0.05 \cdot 10}$

Step 1.5

Combine $120000000$ and $\frac{1}{e^{0.5}}$ .

$500000 + \frac{120000000}{e^{0.5}} + 24000000 e^{- 0.05 \cdot 10}$

Step 1.6

Multiply $- 0.05$ by $10$ .

$500000 + \frac{120000000}{e^{0.5}} + 24000000 e^{- 0.5}$

Step 1.7

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

$500000 + \frac{120000000}{e^{0.5}} + 24000000 \frac{1}{e^{0.5}}$

Step 1.8

Combine $24000000$ and $\frac{1}{e^{0.5}}$ .

$500000 + \frac{120000000}{e^{0.5}} + \frac{24000000}{e^{0.5}}$

Step 2

Combine fractions.

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Step 2.1

Combine the numerators over the common denominator.

$500000 + \frac{120000000 + 24000000}{e^{0.5}}$

Step 2.2

Add $120000000$ and $24000000$ .

$500000 + \frac{144000000}{e^{0.5}}$

Step 3

To write $500000$ as a fraction with a common denominator, multiply by $\frac{e^{0.5}}{e^{0.5}}$ .

$\frac{500000 e^{0.5}}{e^{0.5}} + \frac{144000000}{e^{0.5}}$

Step 4

Combine the numerators over the common denominator.

$\frac{500000 e^{0.5} + 144000000}{e^{0.5}}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$\frac{500000 e^{0.5} + 144000000}{e^{0.5}}$

Decimal Form:

$87840414.9986192$