What is 20*1/8*e^{-0.0675*5} ?

The solution to 20*1/8*e^{-0.0675*5} is 1.78387…

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simplify 201/8e^{-0.0675*5}

simplify

20 \cdot \frac{1}{8} \cdot e^{- 0.0675 \cdot 5}

1.78387 \dots

Solution steps

20 \cdot \frac{1}{8} e^{- 0.0675 \cdot 5}

Apply exponent rule:

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

= 20 \cdot \frac{1}{8} \cdot \frac{1}{e ^{5 \cdot 0.0675}}

Multiply the numbers:

0.0675 \cdot 5 = 0.3375

= 20 \cdot \frac{1}{8} \cdot \frac{1}{e ^{0.3375}}

Multiply fractions:

a \cdot \frac{b}{c} \cdot \frac{d}{e} = \frac{a \cdot b \cdot d}{c \cdot e}

= \frac{1 \cdot 1 \cdot 20}{8 e ^{0.3375}}

Multiply the numbers:

1 \cdot 1 \cdot 20 = 20

= \frac{20}{8 e ^{0.3375}}

Cancel the common factor:

4

= \frac{5}{2 e ^{0.3375}}

e^{0.3375} = 1.40143 \dots

= \frac{5}{2 \cdot 1.40143 \dots}

Multiply the numbers:

2 \cdot 1.40143 \dots = 2.80287 \dots

= \frac{5}{2.80287 \dots}

Divide the numbers:

\frac{5}{2.80287 \dots} = 1.78387 \dots

= 1.78387 \dots

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