簡約-30e^{-0.01(100)}[2-0.01(100)]

解

簡約

- 30 e^{- 0.01 (100)} [2 - 0.01 (100)]

- \frac{30}{e}

十進法表記

- 11.03638 \dots

解答ステップ

- 30 e^{- 0.01 (100)} [2 - 0.01 (100)]

指数の規則を適用する:

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

= - 30 \cdot \frac{1}{e ^{100 \cdot 0.01}} [2 - 100 \cdot 0.01]

e^{0.01 \cdot 100} = e

= - 30 \cdot \frac{1}{e} (2 - 100 \cdot 0.01)

数を乗じる:

0.01 \cdot 100 = 1

= - 30 \cdot \frac{1}{e} (2 - 1)

数を引く:

2 - 1 = 1

= - 30 \cdot 1 \cdot \frac{1}{e}

分数を乗じる:

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

= - 1 \cdot \frac{1 \cdot 30}{e}

数を乗じる:

1 \cdot 30 = 30

= - 1 \cdot \frac{30}{e}

乗算:

1 \cdot \frac{30}{e} = \frac{30}{e}

= - \frac{30}{e}