Thread: Exponential and Logarithmic functions

Consider that the proportion of a radioactive material remaining after time t has elapsed is e^-kt where k is a positive constant; investigate the re;ationship between k and the half-life of the material.

Hey tedwa64.

Do you have the formula for radio-active decay either in function form or in DE form?

Hey Chiro,
Function form.

You have to find the time it takes where the quantity is halved.

So if you set up f(t0) = e^(-kt0) and f(t1) = e^(-kt1) then f(t1) = 1/2*f(t0) for some t1 > t0.

We get 1/2 = e^(-k[t1-t0]). So we get -ln(2) = -k*[t1-t0] which means our half life time is t1-t0 = ln(2)/k.

This is the time it takes for your quantity to reduce in half.