Finite Math Examples

$- 22 + 38 e^{- 0.03 \cdot 18}$

Step 1

Simplify each term.

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Step 1.1

Multiply $- 0.03$ by $18$ .

$- 22 + 38 e^{- 0.54}$

Step 1.2

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

$- 22 + 38 \frac{1}{e^{0.54}}$

Step 1.3

Combine $38$ and $\frac{1}{e^{0.54}}$ .

$- 22 + \frac{38}{e^{0.54}}$

Step 2

To write $- 22$ as a fraction with a common denominator, multiply by $\frac{e^{0.54}}{e^{0.54}}$ .

$- 22 \cdot \frac{e^{0.54}}{e^{0.54}} + \frac{38}{e^{0.54}}$

Step 3

Combine $- 22$ and $\frac{e^{0.54}}{e^{0.54}}$ .

$\frac{- 22 e^{0.54}}{e^{0.54}} + \frac{38}{e^{0.54}}$

Step 4

Combine the numerators over the common denominator.

$\frac{- 22 e^{0.54} + 38}{e^{0.54}}$

Step 5

Factor $- 1$ out of $- 22 e^{0.54}$ .

$\frac{- (22 e^{0.54}) + 38}{e^{0.54}}$

Step 6

Rewrite $38$ as $- 1 (- 38)$ .

$\frac{- (22 e^{0.54}) - 1 (- 38)}{e^{0.54}}$

Step 7

Factor $- 1$ out of $- (22 e^{0.54}) - 1 (- 38)$ .

$\frac{- (22 e^{0.54} - 38)}{e^{0.54}}$

Step 8

Simplify the expression.

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Step 8.1

Rewrite $- (22 e^{0.54} - 38)$ as $- 1 (22 e^{0.54} - 38)$ .

$\frac{- 1 (22 e^{0.54} - 38)}{e^{0.54}}$

Step 8.2

Move the negative in front of the fraction.

$- \frac{22 e^{0.54} - 38}{e^{0.54}}$

Step 9

The result can be shown in multiple forms.

Exact Form:

$- \frac{22 e^{0.54} - 38}{e^{0.54}}$

Decimal Form:

$0.14443359 \dots$