What is 90000(7-2)e^{-0.2(7)} ?

The solution to 90000(7-2)e^{-0.2(7)} is 110968.63377…

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simplify 90000(7-2)e^{-0.2(7)}

simplify

90000 (7 - 2) e^{- 0.2 (7)}

110968.63377 \dots

Solution steps

90000 (7 - 2) e^{- 0.2 (7)}

Apply exponent rule:

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

= 90000 \cdot \frac{1}{e ^{7 \cdot 0.2}} (7 - 2)

Subtract the numbers:

7 - 2 = 5

= 90000 \cdot 5 \cdot \frac{1}{e ^{7 \cdot 0.2}}

Multiply the numbers:

0.2 \cdot 7 = 1.4

= 90000 \cdot 5 \cdot \frac{1}{e ^{1.4}}

Multiply fractions:

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

= \frac{1 \cdot 90000 \cdot 5}{e ^{1.4}}

Multiply the numbers:

1 \cdot 90000 \cdot 5 = 450000

= \frac{450000}{e ^{1.4}}

e^{1.4} = 4.05519 \dots

= \frac{450000}{4.05519 \dots}

Divide the numbers:

\frac{450000}{4.05519 \dots} = 110968.63377 \dots

= 110968.63377 \dots

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What is 90000(7-2)e^{-0.2(7)} ?
The solution to 90000(7-2)e^{-0.2(7)} is 110968.63377…