Finite Math Examples

$s (9.6) = 11.65 (1 - e^{- \frac{t}{1.27}})$

Step 1

Divide each term in $s (9.6) = 11.65 (1 - e^{- \frac{t}{1.27}})$ by $9.6$ .

$\frac{s \cdot 9.6}{9.6} = \frac{11.65 (1 - e^{- \frac{t}{1.27}})}{9.6}$

Step 2

Simplify the left side.

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Step 2.1

Cancel the common factor of $9.6$ .

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Step 2.1.1

Cancel the common factor.

$\frac{s \cdot 9.6}{9.6} = \frac{11.65 (1 - e^{- \frac{t}{1.27}})}{9.6}$

Step 2.1.2

Divide $s$ by $1$ .

$s = \frac{11.65 (1 - e^{- \frac{t}{1.27}})}{9.6}$

Step 3

Simplify the right side.

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Step 3.1

Simplify the numerator.

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Step 3.1.1

Multiply by $1$ .

$s = \frac{11.65 (1 - e^{- \frac{1 t}{1.27}})}{9.6}$

Step 3.1.2

Factor $1.27$ out of $1.27$ .

$s = \frac{11.65 (1 - e^{- \frac{1 t}{1.27 (1)}})}{9.6}$

Step 3.1.3

Separate fractions.

$s = \frac{11.65 (1 - e^{- (\frac{1}{1.27} \cdot \frac{t}{1})})}{9.6}$

Step 3.1.4

Divide $1$ by $1.27$ .

$s = \frac{11.65 (1 - e^{- (0.78740157 \frac{t}{1})})}{9.6}$

Step 3.1.5

Divide $t$ by $1$ .

$s = \frac{11.65 (1 - e^{- (0.78740157 t)})}{9.6}$

Step 3.1.6

Multiply $0.78740157$ by $- 1$ .

$s = \frac{11.65 (1 - e^{- 0.78740157 t})}{9.6}$

Step 3.2

Factor $9.6$ out of $9.6$ .

$s = \frac{11.65 (1 - e^{- 0.78740157 t})}{9.6 (1)}$

Step 3.3

Separate fractions.

$s = \frac{11.65}{9.6} \cdot \frac{1 - e^{- 0.78740157 t}}{1}$

Step 3.4

Simplify the expression.

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Step 3.4.1

Divide $11.65$ by $9.6$ .

$s = 1.213541\overline{6} \frac{1 - e^{- 0.78740157 t}}{1}$

Step 3.4.2

Divide $1 - e^{- 0.78740157 t}$ by $1$ .

$s = 1.213541\overline{6} (1 - e^{- 0.78740157 t})$

Step 3.5

Apply the distributive property.

$s = 1.213541\overline{6} \cdot 1 + 1.213541\overline{6} (- e^{- 0.78740157 t})$

Step 3.6

Multiply.

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Step 3.6.1

Multiply $1.213541\overline{6}$ by $1$ .

$s = 1.213541\overline{6} + 1.213541\overline{6} (- e^{- 0.78740157 t})$

Step 3.6.2

Multiply $- 1$ by $1.213541\overline{6}$ .

$s = 1.213541\overline{6} - 1.213541\overline{6} e^{- 0.78740157 t}$