Finite Math Examples

f (x) = 0.02 (1 - e^{- 0.2 \cdot 5})

$f (x) = 0.02 (1 - e^{- 0.2 \cdot 5})$

Step 1

Set

0.02 (1 - e^{- 0.2 \cdot 5})

$0.02 (1 - e^{- 0.2 \cdot 5})$ equal to

0

$0$ .

0.02 (1 - e^{- 0.2 \cdot 5}) = 0

$0.02 (1 - e^{- 0.2 \cdot 5}) = 0$

Step 2

Solve for

x

$x$ .

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Step 2.1

Simplify

0.02 (1 - {(2.71828182)}^{- 0.2 \cdot 5})

$0.02 (1 - {(2.71828182)}^{- 0.2 \cdot 5})$ .

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Step 2.1.1

Simplify each term.

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Step 2.1.1.1

Multiply

- 0.2

$- 0.2$ by

5

$5$ .

0.02 (1 - {2.71828182}^{- 1}) = 0

$0.02 (1 - {2.71828182}^{- 1}) = 0$

Step 2.1.1.2

Rewrite the expression using the negative exponent rule

b^{- n} = \frac{1}{b^{n}}

$b^{- n} = \frac{1}{b^{n}}$ .

0.02 (1 - \frac{1}{2.71828182}) = 0

$0.02 (1 - \frac{1}{2.71828182}) = 0$

Step 2.1.1.3

Divide

1

$1$ by

2.71828182

$2.71828182$ .

0.02 (1 - 1 \cdot 0.36787944) = 0

$0.02 (1 - 1 \cdot 0.36787944) = 0$

Step 2.1.1.4

Multiply

- 1

$- 1$ by

0.36787944

$0.36787944$ .

0.02 (1 - 0.36787944) = 0

$0.02 (1 - 0.36787944) = 0$

0.02 (1 - 0.36787944) = 0

$0.02 (1 - 0.36787944) = 0$

Step 2.1.2

Simplify the expression.

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Step 2.1.2.1

Subtract

0.36787944

$0.36787944$ from

1

$1$ .

0.02 \cdot 0.63212055 = 0

$0.02 \cdot 0.63212055 = 0$

Step 2.1.2.2

Multiply

0.02

$0.02$ by

0.63212055

$0.63212055$ .

0.01264241 = 0

$0.01264241 = 0$

0.01264241 = 0

$0.01264241 = 0$

0.01264241 = 0

$0.01264241 = 0$

Step 2.2

Since

0.01264241 \neq 0

$0.01264241 \neq 0$ , there are no solutions.

No solution

No solution

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$