What is 20*1/8*e^{-0.0675*3} ?

The solution to 20*1/8*e^{-0.0675*3} is 2.04171…

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simplify 201/8e^{-0.0675*3}

simplify

20 \cdot \frac{1}{8} \cdot e^{- 0.0675 \cdot 3}

2.04171 \dots

Solution steps

20 \cdot \frac{1}{8} e^{- 0.0675 \cdot 3}

Apply exponent rule:

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

= 20 \cdot \frac{1}{8} \cdot \frac{1}{e ^{3 \cdot 0.0675}}

Multiply the numbers:

0.0675 \cdot 3 = 0.2025

= 20 \cdot \frac{1}{8} \cdot \frac{1}{e ^{0.2025}}

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 ^{0.2025}}

Multiply the numbers:

1 \cdot 1 \cdot 20 = 20

= \frac{20}{8 e ^{0.2025}}

Cancel the common factor:

4

= \frac{5}{2 e ^{0.2025}}

e^{0.2025} = 1.22446 \dots

= \frac{5}{2 \cdot 1.22446 \dots}

Multiply the numbers:

2 \cdot 1.22446 \dots = 2.44892 \dots

= \frac{5}{2.44892 \dots}

Divide the numbers:

\frac{5}{2.44892 \dots} = 2.04171 \dots

= 2.04171 \dots

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