just... don't do this.

stupid_e.py

In [1]: class RaiseEWithCaret(object):
   ...:     def __xor__(self, exponent):
   ...:         from math import exp
   ...:         return exp(exponent)
   ...:     

In [2]: e = RaiseEWithCaret()

In [3]: e^1
Out[3]: 2.718281828459045

In [4]: decay = lambda k, t: e^(-k * t)

In [5]: [decay(0.25, t) for t in range(10)]
Out[5]: 
[1.0,
 0.7788007830714049,
 0.6065306597126334,
 0.4723665527410147,
 0.36787944117144233,
 0.2865047968601901,
 0.22313016014842982,
 0.17377394345044514,
 0.1353352832366127,
 0.10539922456186433]

In [6]: e^1 * 0
Out[6]: 1.0

In [7]: ummmmmmmm...