Finite Math Examples

$2 = 2 (1 - e^{- 0.037 t})$

Step 1

Rewrite the equation as $2 (1 - e^{- 0.037 t}) = 2$ .

$2 (1 - e^{- 0.037 t}) = 2$

Step 2

Simplify $2 (1 - e^{- 0.037 t})$ .

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Step 2.1

Apply the distributive property.

$2 \cdot 1 + 2 (- e^{- 0.037 t}) = 2$

Step 2.2

Multiply.

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Step 2.2.1

Multiply $2$ by $1$ .

$2 + 2 (- e^{- 0.037 t}) = 2$

Step 2.2.2

Multiply $- 1$ by $2$ .

$2 - 2 e^{- 0.037 t} = 2$

Step 3

Move all terms not containing $t$ to the right side of the equation.

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Step 3.1

Subtract $2$ from both sides of the equation.

$- 2 e^{- 0.037 t} = 2 - 2$

Step 3.2

Subtract $2$ from $2$ .

$- 2 e^{- 0.037 t} = 0$

Step 4

Divide each term in $- 2 e^{- 0.037 t} = 0$ by $- 2$ and simplify.

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Step 4.1

Divide each term in $- 2 e^{- 0.037 t} = 0$ by $- 2$ .

$\frac{- 2 e^{- 0.037 t}}{- 2} = \frac{0}{- 2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 2$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 2 e^{- 0.037 t}}{- 2} = \frac{0}{- 2}$

Step 4.2.1.2

Divide $e^{- 0.037 t}$ by $1$ .

$e^{- 0.037 t} = \frac{0}{- 2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $0$ by $- 2$ .

$e^{- 0.037 t} = 0$

Step 5

Take the natural logarithm of both sides of the equation to remove the variable from the exponent.

$\ln (e^{- 0.037 t}) = \ln (0)$

Step 6

The equation cannot be solved because $\ln (0)$ is undefined.

Undefined

Step 7

There is no solution for $e^{- 0.037 t} = 0$

No solution