Exponential Growth & Decay

Question

2). Find the half-life of a radioactive element, which decays according to the function A(t) = A₀e^-0.0226t where t is the time in years

Answer 1

Pretty straightforward.

The half life of a radioactive substance is the amount of time needed for the sample to decay to half its original size.

1. set A(t) = half the original amount (A₀)/2),
2. divide out A₀,
3. take the natural log (ln) of both sides and
4. solve for t.