In 1986 it was determined that the Challenger disaster was caused by failure of the primary O-rings. Linda Tappin gives a formula in "Analyzing Data Relating to the Disaster" (The Mathematics Teacher, Vol. 87, No. 6, Sept. 1994, ) that relates the temperature \(x\) (in degrees Fahrenheit) around the O-rings and the expected number \(y\) of eroded or leaky primary O-rings:

\[y=\frac{6 e^{5.085-0.1156 x}}{1+e^{5.085-0.1156 x}}\]

Do some research on the Challenger disaster and, in particular, its relationship to this formula.