What is 100e^{-(0.031)(20)} ?

The solution to 100e^{-(0.031)(20)} is 53.79444…

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simplify 100e^{-(0.031)(20)}

simplify

100 e^{- (0.031) (20)}

53.79444 \dots

Solution steps

100 e^{- (0.031) (20)}

Apply exponent rule:

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

= 100 \cdot \frac{1}{e ^{20 \cdot 0.031}}

Multiply the numbers:

0.031 \cdot 20 = 0.62

= 100 \cdot \frac{1}{e ^{0.62}}

Multiply fractions:

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

= \frac{1 \cdot 100}{e ^{0.62}}

Multiply the numbers:

1 \cdot 100 = 100

= \frac{100}{e ^{0.62}}

e^{0.62} = 1.85892 \dots

= \frac{100}{1.85892 \dots}

Divide the numbers:

\frac{100}{1.85892 \dots} = 53.79444 \dots

= 53.79444 \dots

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