Anyone know anything about half lives?

Question

Exponential decaying substance decreases by 32% in 10 hours. What is the half life of the substance?

Answer 1

P=P_0 2^(-t/T)
where P_0 is the original amount and T is the half-life.

When t=10, you have P=(1-.32)P_0=.68P_0,
so
.68=2^(-10/T).
Now solve for T:
ln(.68)=(10/T)ln(2), so
T=-10*ln(2)/ln(.68)=18hrs.

Answer 2

0.68 = r^10 ......... amount remaining
0.50 = r^x

log (0.68) = 10 log r
log (0.50) = x log r

log (0.68) .. 10
------------- = --- ........ pretty proportion
log (0.50) ... x

x = 10 log (0.50) / log (0.68)
x = 17.97 hr