簡約 100e^{(-5.0765*10^{-3})}

解

簡約

100 e^{(- 5.0765 \cdot 1 0^{- 3})}

99.49363 \dots

解答ステップ

100 e^{(- 5.0765 \cdot 1 0^{- 3})}

指数の規則を適用する:

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

= 100 \cdot \frac{1}{e ^{1 0^{- 3} \cdot 5.0765}}

\frac{1}{e ^{5.0765 \cdot 1 0^{- 3}}} = \frac{1}{e ^{0.0050765}}

= 100 \cdot \frac{1}{e ^{0.0050765}}

分数を乗じる:

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

= \frac{1 \cdot 100}{e ^{0.0050765}}

数を乗じる:

1 \cdot 100 = 100

= \frac{100}{e ^{0.0050765}}

e^{0.0050765} = 1.00508 \dots

= \frac{100}{1.00508 \dots}

数を割る:

\frac{100}{1.00508 \dots} = 99.49363 \dots

= 99.49363 \dots