What is 200e^{-0.4(2)} ?

The solution to 200e^{-0.4(2)} is 89.86579…

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simplify 200e^{-0.4(2)}

simplify

200 e^{- 0.4 (2)}

89.86579 \dots

Solution steps

200 e^{- 0.4 (2)}

Apply exponent rule:

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

= 200 \cdot \frac{1}{e ^{2 \cdot 0.4}}

Multiply the numbers:

0.4 \cdot 2 = 0.8

= 200 \cdot \frac{1}{e ^{0.8}}

Multiply fractions:

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

= \frac{1 \cdot 200}{e ^{0.8}}

Multiply the numbers:

1 \cdot 200 = 200

= \frac{200}{e ^{0.8}}

e^{0.8} = 2.22554 \dots

= \frac{200}{2.22554 \dots}

Divide the numbers:

\frac{200}{2.22554 \dots} = 89.86579 \dots

= 89.86579 \dots

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