An initial amount of 500 g of a certain radioactive substance decays according to A(t)=500e^-.0333t Where tea is measured in years find the half-life of the substance.

Question

An initial amount of 500 g of a certain radioactive substance decays according to A(t)=500e^-.0333t Where t is measured in years find the half-life of the substance.

How do I solve this? It’s on my homework, but when I look through my notes I don’t have this formula in it, and I don’t know how to solve it.

Answer 1

The half-life of a substance is the time it takes for half of the initial amount of substance to decay. Hence, we solve for t when A(t) = 500/2 = 250:

250 = 500e^-0.0333t

1/2 = e^-0.0333t

ln(1/2) = -0.0333t

ln(1/2)/(-0.0333) = t

t ≈ 20.8

Therefore, the half-life of the substance is about 20.8 years.

Hope this helped!