Calculus Examples

$0.08 + 0.12 (1 - e^{- 0.02 \cdot 20})$

Step 1

Simplify each term.

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Step 1.1

Simplify each term.

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Step 1.1.1

Multiply $- 0.02$ by $20$ .

$0.08 + 0.12 (1 - e^{- 0.4})$

Step 1.1.2

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

$0.08 + 0.12 (1 - \frac{1}{e^{0.4}})$

Step 1.2

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

$0.08 + 0.12 (\frac{e^{0.4}}{e^{0.4}} - \frac{1}{e^{0.4}})$

Step 1.3

Combine the numerators over the common denominator.

$0.08 + 0.12 \frac{e^{0.4} - 1}{e^{0.4}}$

Step 1.4

Multiply $0.12 \frac{e^{0.4} - 1}{e^{0.4}}$ .

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Step 1.4.1

Combine $0.12$ and $\frac{e^{0.4} - 1}{e^{0.4}}$ .

$0.08 + \frac{0.12 (e^{0.4} - 1)}{e^{0.4}}$

Step 1.4.2

Multiply $0.12$ by $e^{0.4} - 1$ .

$0.08 + \frac{0.05901896}{e^{0.4}}$

Step 1.5

Replace $e$ with an approximation.

$0.08 + \frac{0.05901896}{{2.71828182}^{0.4}}$

Step 1.6

Raise $2.71828182$ to the power of $0.4$ .

$0.08 + \frac{0.05901896}{1.49182469}$

Step 1.7

Divide $0.05901896$ by $1.49182469$ .

$0.08 + 0.03956159$

Step 2

Add $0.08$ and $0.03956159$ .

$0.11956159$