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.
 
Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
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