Question

PLEASE HELP. A substance decays according the the equation ae^-0.0025t, where t is in minutes. Find the half life of the substance. Round to the nearest tenth.

Answer 1

First of all, that's not an equation.  An equation needs an 'equals' sign ( = ),
so you need something like 

               Amount present = a e^-0.0025t .

                                   'a' = amount present when t = 0 .

The half-life is the time it takes for the original amount to decay to half of it.

That's just 't' when                      e^-0.0025t  =  1/2

Take the natural log of each side:    -0.0025t  =  ln(0.5)

Divide each side by  -0.0025 :        t = ln(0.5) / (-0.0025) =

                                                     (-0.69315) / (-0.0025) =

                                                   t  =  277.26 minutes

                                                    ( 4hrs 37min 15.5sec)

Rounded to nearest tenth:  t = 277.3 minutes .