# Math Help - Exponential and Logarithmic functions

1. ## 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.

2. ## Re: Exponential and Logarithmic functions

Hey tedwa64.

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

3. ## Re: Exponential and Logarithmic functions

Hey Chiro,
Function form.

4. ## Re: Exponential and Logarithmic functions

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.