# Math Help - Exponential Integration question

1. ## Exponential Integration question

For question 15, so far, I have got the following

dN/N = -k dt

From there, I get N(0)e-kt

I solved k to be 0.0001216 that was using k = -ln(1/2)/5700 ==> (ln 2)/5700
then N(t) = N(0)e-(ln 2)t/5700
which is also N(t) = N(0)*-2t/5700

So I am getting close, but what is N(0)?
so to do the part b I solve N(t) = N(0)*-20.4(5700) - but what is N(0)?

Question 16 I have solved, don't have any issues with that.

2. ## Re: Exponential Integration question

There is a little mistake in the indices of the equation you derived, you brought back the minus sign after changing -ln(1/2) to ln(2) so the equation is
$N(0)e^{\frac{ln(2)t}{5700}}$

The 40% is related to number of atoms not time, if it decays to 40% of its original size after a time T then 0.4*N(0)= N(T)
Using the equation you derived,

$0.4N(0)=N(0)e^{\frac{ln(2)T}{5700}}$

The N(0) cancels on both sides.