Half Life Problem

Question

A radioactive substance used in nuclear weapons decays at the rate of 4.3​% per year. Calculate the​ half-life of the radioactive substance.

Answer 1

Start by writing a continuous decay equation: A = Be^-.043t.

Now pick values for A and B, which are the ending and beginning amounts, respectively. It doesn't matter what values you use, as long as A is half of B:

1 = 2e^-.043t.

Now divide both sides by 2:

0.5 = e^-.043t.

Take the ln of both sides:

ln(0.5) = ln(e^-.043t.)

Use log properties to simplify:

ln(0.5) = -.043t

Divide both sides by -.043 and you will have your answer.