e^-(1+0.1*(x-0.5)/0.2)^(-1/0.1)=0.99
You asked:
Investigate the equation: \({e}^{-{\left( 1 + \frac{0.1 \cdot \left(x - 0.5\right)}{0.2} \right)}^{\frac{-1}{0.1}}} = 0.99\).
MathBot Answer:
The 2 solutions to the equation are: \[\begin{aligned}x &= - \frac{3}{2} + \frac{2}{\sqrt[10]{- \log{\left(\frac{99}{100} \right)}}} \approx 1.6681952\\x &= - \frac{3}{2} - \frac{2}{\sqrt[10]{- \log{\left(\frac{99}{100} \right)}}} \approx -4.6681952\end{aligned}\]
\(e\) is Euler's number, a mathematical constant that is approximately \(2.71828\).