(20)/(1+125e^(-0.8(6.413)))

asked by guest
on Nov 26, 2024 at 6:22 pm



You asked:

Evaluate the expression: \(\frac{20}{1 + 125 {e}^{-\left( 0.8 \cdot 6.413 \right)}}\)

MathBot Answer:

\[\frac{20}{1 + 125 {e}^{-\left( 0.8 \cdot 6.413 \right)}} = \frac{20}{\frac{125}{e^{\frac{6413}{1250}}} + 1} \approx 11.4990488337761165987858946651385\]

\[\begin{aligned}\frac{20}{1 + 125 {e}^{-\left( 0.8 \cdot 6.413 \right)}}& = 20 \cdot \frac{1}{1 + 125 \cdot e^{- \frac{8}{10} \cdot \left(6 + \frac{413}{1000}\right)}}\\& = 20 \cdot \frac{1}{1 + 125 \cdot e^{- \frac{8}{10} \cdot \frac{6413}{1000}}}\\& = 20 \cdot \frac{1}{1 + 125 \cdot e^{- \frac{4}{5} \cdot \frac{6413}{1000}}}\\& = 20 \cdot \frac{1}{1 + 125 \cdot e^{- \frac{6413}{1250}}}\\& = 20 \cdot \frac{1}{1 + 125 \cdot \frac{1}{e^{\frac{6413}{1250}}}}\\& = 20 \cdot \frac{1}{1 + 125 \cdot e^{- \frac{6413}{1250}}}\end{aligned}\]

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

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