Question

The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of per day. Find the half-life of this substance (that is, the time it takes for one-half the original amount in a given sample of this substance to decay).

Answer 1

t = ln(0.5)/-r

Explanation:

The decay rate parameter is missing. I will assume a value of 4% per day.

The exponential decay is modeled by the following equation:

A = A0*e^(-r*t)

where A is the mass after t time (in days), A0 is the initial mass and r is the rate (as a decimal).

At half-life A = A0/2, then:

A0/2 = A0*e^(-0.04*t)

0.5 = e^(-0.04*t)

ln(0.5) = -0.04*t

t = ln(0.5)/-0.04

t = 17.33 days

In general the half-life time is:

t = ln(0.5)/-r