# Exponential and Logarithmic functions

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• Mar 5th 2013, 11:57 PM
tedwa64
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.
• Mar 6th 2013, 12:07 AM
chiro
Re: Exponential and Logarithmic functions
Hey tedwa64.

Do you have the formula for radio-active decay either in function form or in DE form?
• Mar 6th 2013, 12:11 AM
tedwa64
Re: Exponential and Logarithmic functions
Hey Chiro,
Function form.
• Mar 6th 2013, 12:26 AM
chiro
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.