What is e^{-0.01}[0.3417(0.5898)+0.6583(0.1923)] ?

The solution to e^{-0.01}[0.3417(0.5898)+0.6583(0.1923)] is 0.32486…

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simplify e^{-0.01}[0.3417(0.5898)+0.6583(0.1923)]

simplify

e^{- 0.01} [0.3417 (0.5898) + 0.6583 (0.1923)]

0.32486 \dots

Solution steps

e^{- 0.01} [0.3417 (0.5898) + 0.6583 (0.1923)]

Apply exponent rule:

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

= \frac{1}{e ^{0.01}} [0.3417 \cdot 0.5898 + 0.6583 \cdot 0.1923]

Multiply the numbers:

0.3417 \cdot 0.5898 = 0.20153466

= \frac{1}{e ^{0.01}} (0.20153466 + 0.6583 \cdot 0.1923)

Multiply the numbers:

0.6583 \cdot 0.1923 = 0.12659109

= \frac{1}{e ^{0.01}} (0.20153466 + 0.12659109)

Add the numbers:

0.20153466 + 0.12659109 = 0.32812575

= 0.32812575 \cdot \frac{1}{e ^{0.01}}

Multiply fractions:

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

= \frac{1 \cdot 0.32812575}{e ^{0.01}}

Multiply the numbers:

1 \cdot 0.32812575 = 0.32812575

= \frac{0.32812575}{e ^{0.01}}

e^{0.01} = 1.01005 \dots

= \frac{0.32812575}{1.01005 \dots}

Divide the numbers:

\frac{0.32812575}{1.01005 \dots} = 0.32486 \dots

= 0.32486 \dots

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e^{- 3 t} u (t - 2)

What is e^{-0.01}[0.3417(0.5898)+0.6583(0.1923)] ?
The solution to e^{-0.01}[0.3417(0.5898)+0.6583(0.1923)] is 0.32486…