A collection of schmutz decays according to the equation y=ae^-0.0358t where t is in days. Find the half life of this schmutz collection.
so you are looking for
ae^-0.0358t = .5a
e^-0.0358t = .5
take ln of both sides, and recall ln e = 1
-.0358t = ln .5
t = ln .5/-.0358 = .....