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

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.