Continuously compounded interest

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Homework Statement


I must give medication to a patient continuously, but at the same time the kidneys eliminate the 2,5 per cent of the medication. I need to have 90micrograms of medication at the end of 4 hours. The initial medication amount is zero.
Normally, the limit of the compound intereset formula must be taken.


Homework Equations


The formula for continuous compounding is
Mfinal = Minitial x e^(rt)

The Attempt at a Solution


Mfinal is 90, r is -0,025, t is four and I need to find Minitial. Or is r 0,975. I try to solve the equation. I feel that I must find the rate first, like ln(Mfinal/Minitial)/t; but I can't without the initial value. Please help.
 
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ok I sorted it out. sorry to bother.
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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