1.85*10^-12* exp(-1690/281.7)

asked by guest
on Nov 14, 2024 at 12:23 am



You asked:

Evaluate the expression: \(1.85 \cdot {10}^{-12} \cdot {e}^{\frac{-1690}{281.7}}\)

MathBot Answer:

\[1.85 \cdot {10}^{-12} \cdot {e}^{\frac{-1690}{281.7}} = \frac{37}{20000000000000 e^{\frac{16900}{2817}}} \approx 4.58894840988257885 \cdot 10^{-15}\]

\[\begin{aligned}1.85 \cdot {10}^{-12} \cdot {e}^{\frac{-1690}{281.7}}& = \left(1 + \frac{85}{100}\right) \cdot \frac{1}{10^{12}} \cdot e^{-1690 \cdot \frac{1}{281 + \frac{7}{10}}}\\& = \left(1 + \frac{17}{20}\right) \cdot \frac{1}{10^{12}} \cdot e^{-1690 \cdot \frac{1}{281 + \frac{7}{10}}}\\& = \frac{37}{20} \cdot \frac{1}{10^{12}} \cdot e^{-1690 \cdot \frac{1}{281 + \frac{7}{10}}}\\& = \frac{37}{20} \cdot \frac{1}{1000000000000} \cdot e^{-1690 \cdot \frac{1}{281 + \frac{7}{10}}}\\& = \frac{37}{20} \cdot \frac{1}{1000000000000} \cdot e^{-1690 \cdot \frac{1}{\frac{2817}{10}}}\\& = \frac{37}{20} \cdot \frac{1}{1000000000000} \cdot \frac{1}{e^{\frac{16900}{2817}}}\\& = \frac{37}{20} \cdot \frac{1}{1000000000000} \cdot e^{- \frac{16900}{2817}}\\& = \frac{37}{20000000000000} \cdot e^{- \frac{16900}{2817}}\end{aligned}\]

\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).

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