Trigonometry Examples

$2 = 10 e^{- 0.0231} t$

Step 1

Rewrite the equation as $10 e^{- 0.0231} t = 2$ .

$10 e^{- 0.0231} t = 2$

Step 2

Simplify.

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Step 2.1

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

$10 \frac{1}{e^{0.0231}} t = 2$

Step 2.2

Combine $10$ and $\frac{1}{e^{0.0231}}$ .

$\frac{10}{e^{0.0231}} t = 2$

Step 3

Multiply each term in $\frac{10}{e^{0.0231}} t = 2$ by $\frac{e^{0.0231}}{10}$ to eliminate the fractions.

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Step 3.1

Multiply each term in $\frac{10}{e^{0.0231}} t = 2$ by $\frac{e^{0.0231}}{10}$ .

$\frac{10}{e^{0.0231}} t \frac{e^{0.0231}}{10} = 2 \frac{e^{0.0231}}{10}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Combine $\frac{10}{e^{0.0231}}$ and $t$ .

$\frac{10 t}{e^{0.0231}} \cdot \frac{e^{0.0231}}{10} = 2 \frac{e^{0.0231}}{10}$

Step 3.2.2

Combine.

$\frac{10 t e^{0.0231}}{e^{0.0231} \cdot 10} = 2 \frac{e^{0.0231}}{10}$

Step 3.2.3

Cancel the common factor of $10$ .

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Step 3.2.3.1

Cancel the common factor.

$\frac{10 t e^{0.0231}}{e^{0.0231} \cdot 10} = 2 \frac{e^{0.0231}}{10}$

Step 3.2.3.2

Rewrite the expression.

$\frac{t e^{0.0231}}{e^{0.0231}} = 2 \frac{e^{0.0231}}{10}$

Step 3.2.4

Cancel the common factor of $e^{0.0231}$ .

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Step 3.2.4.1

Cancel the common factor.

$\frac{t e^{0.0231}}{e^{0.0231}} = 2 \frac{e^{0.0231}}{10}$

Step 3.2.4.2

Divide $t$ by $1$ .

$t = 2 \frac{e^{0.0231}}{10}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Cancel the common factor of $2$ .

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Step 3.3.1.1

Factor $2$ out of $10$ .

$t = 2 \frac{e^{0.0231}}{2 (5)}$

Step 3.3.1.2

Cancel the common factor.

$t = 2 \frac{e^{0.0231}}{2 \cdot 5}$

Step 3.3.1.3

Rewrite the expression.

$t = \frac{e^{0.0231}}{5}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$t = \frac{e^{0.0231}}{5}$

Decimal Form:

$t = 0.20467377 \dots$