Question

The concentration of an isotope is 1/500 of its initial value after one day. What is the rate of decay?

Answer 1

The exponential growth/decay formula is given by A = Pe^(rt), where A is the final amount, P is the initial amount, r is the rate of growth/decay and t is time. 

We are given A = (1/500)P and t=1, so substituting:
(1/500)P = Pe^(r*1)
Cancelling out P on both sides:
1/500 = e^r
ln(1/500) = ln(e^r)
r = -6.215

Rate of decay is -6.215 per day.