Equation that gives the probability of nausea in surgical patients

I found this research article explaining how the attached .jpg is calculated but I cannot figure it out.

This is an equation that gives the probability of nausea in surgical patients.

As explained by the researcher: "The root logic behind the equation (1.jpg) is based on Logistic regression to model the relation between explanatory variables and binary outcome variables. The logistic regression modeling assumes that the probability of an event (i.e., the occurrence of the outcome) is associated with the values of the explanatory variables in the following way shown in 1.jpg where 2.jpg where p = probability of the occurrence of the outcome, xi = value of the ith independent variable, and [Greek small letter beta]i events for any patient = parameter estimates for the ith variable."

He continues:

"Fitting the model to the data, we can obtain the maximum likelihood estimate of the parameters for each variable. Based on the maximum likelihood estimates from the final models, it is possible to calculate an expected risk of occurrence of the specific adverse event for any patient. 3.jpg where:
Age = age in years/10
Sex = 1 if male and 0 if female;
Smoke = 1 if smoker and 0 if nonsmoker;
PONV History = 1 if previous PONV and 0 if no previous PONV;
Duration = duration of surgery in 30-min increments;
GA = 1 if general anesthesia and 0 if other type of anesthesia;
ENT = 1 if ENT and 0 if other type of surgery;
Ophthalm = 1 if ophthalmology and 0 if other type of surgery;
Plastic = 1 if plastic surgery and 0 if other type of surgery;
GynNonDC = 1 if gynecologic non D&C procedure and 0 if other type of surgery;
OrtKnee = 1 if orthopedic procedure involving knee and 0 if other type of surgery; OrtShoulder = 1 if orthopedic procedure involving the shoulder and 0 if other type of surgery;
OrtOther = 1 if orthopedic procedure involving neither knee nor shoulder and 0 if other type of surgery."

I understand the "1 and 0" explained above for the specific patient and/or procedure type.

I just can't make the equation (as given) work....... what does "e" represent in the equation?

Examples

The risk for patient 5, a 22-yr-old woman with a history of smoking and previous PONV undergoing a 90-min bilateral breast augmentation (plastic surgery) with general anesthesia is 52% (4.jpg)

The source of the link is here where the explanation is in the appendix http://www.anesthesiology.org/pt/re/anes/fulltext.00000542-199907000-00018.htm;jsessionid=CzPXRpljE9Ft2PZqkXNBbIPMF1XvsRXRNRQ1hlwBpVHuY2MowR2O!1988335901!-949856145!9001!-1#ME6

Could someone please explain this to me on how 52% is obtained?

Thank You

Anthony