Half life Question?

Question

The activity of a sample drops by a factor of 10 in 8.0 minutes. What is its half-life?
_______________ min

Answer 1

OMG it's dead! It's going fast. It has not have a full life... :-(

We can start with a sample on size A and in time t this what is left
A(t)=Aexp(-at)

t= 0 min A(0)=A
t=8 min A(8)=A/10
so substituting time and what we know we have
A/10=Aexp(-a8)
-ln(10)= -a8
a= ln(10) /8

also we can say that fro 1/2 life (half is dead and half is alive!)
(1/2)A=Aexp(-[ln(10)/8] t)
-ln(2)= (-[ln(10)/8] t
t(half life)=ln(2)/[ln(10)/8]
t(1/2)= 2.41 min = 144 s

In general the equation for half life is

t(1/2) = ln(2)/a a - time constant of decay