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).

t = ln (0.5) / -r

Step-by-step 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