Exponents and logs: a decay equation from a half life.

Tutoring math, you see exponential growth and decay. The tutor mentions an equation from a half life.

Example: a specimen loses half activity every 45 days. Find a equation for it.

Answer: The equation will be of the form P = P_oe^(kt), t in days, where P_o is the starting amount and P is the amount at time t. At the half life, P=P_o/2, leaving

1/2 = e^(45k).

Taking ln (natural log) of both sides, we get

ln(1/2) = 45k. Then, since ln(1/2) = -ln2,

-(ln2)/45 = k