Continuously compounded interest

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SUMMARY

The discussion revolves around calculating the initial medication amount required to achieve a final dose of 90 micrograms after 4 hours, considering a continuous elimination rate of 2.5%. The relevant formula for continuous compounding, Mfinal = Minitial x e^(rt), is applied, where Mfinal is 90, r is -0.025, and t is 4. The user initially struggled with determining Minitial but later resolved the issue independently.

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  • Understanding of continuous compounding formulas
  • Familiarity with exponential functions
  • Basic knowledge of pharmacokinetics
  • Ability to solve logarithmic equations
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  • Study the derivation of the continuous compounding formula
  • Learn about pharmacokinetic models for drug elimination
  • Explore applications of exponential functions in real-world scenarios
  • Investigate the impact of varying elimination rates on medication dosing
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This discussion is beneficial for healthcare professionals, pharmacologists, and students studying pharmacokinetics or mathematical modeling in medicine.

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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.
 

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