What is 0.1e^{-0.1(6)} ?

The solution to 0.1e^{-0.1(6)} is 0.05488…

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simplify 0.1e^{-0.1(6)}

simplify

0.1 e^{- 0.1 (6)}

0.05488 \dots

Solution steps

0.1 e^{- 0.1 (6)}

Apply exponent rule:

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

= 0.1 \cdot \frac{1}{e ^{6 \cdot 0.1}}

Multiply the numbers:

0.1 \cdot 6 = 0.6

= 0.1 \cdot \frac{1}{e ^{0.6}}

Multiply fractions:

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

= \frac{1 \cdot 0.1}{e ^{0.6}}

Multiply the numbers:

1 \cdot 0.1 = 0.1

= \frac{0.1}{e ^{0.6}}

e^{0.6} = 1.82211 \dots

= \frac{0.1}{1.82211 \dots}

Divide the numbers:

\frac{0.1}{1.82211 \dots} = 0.05488 \dots

= 0.05488 \dots

(40) (1.6 \cdot 1 0^{- 19})

3.1 \cdot 1 0^{- 11} m

8 e^{- 100 (5)} (3.2)

e^{- m t} (a sin (wt) + b cos (wt))