Find the half-life of a radioactive substance that decays at a continuous rate of 13 % per minute.

Answer 1

Using A = A₀(1 - r)^t where A is the amount that we have of a substance at any time (t), A₀ is the amount we start with (at t = 0), and r is thr rate at which it is decaying, then we can say:

(1/2)A₀ = A₀(1 - 0.13)^t [dividing both sides by A₀ gives us:

1/2 = (0.87)^t [taking the log of both sides gives us:

log(1/2) = log(0.87)^t [then using a logarithm property we can move the "t" out front giving us:

log(1/2) = t•log(0.87) [then dividing both sides by log(0.87) gives us:

log(1/2)/log(0.87) = t [then plugging this into a calculator we get:

t = 4.977 minutes

So the half-life (the time it takes for half of the material to decay) is 4.977 minutes (about 5 minutes)