   Chapter 7.8, Problem 70E

Chapter
Section
Textbook Problem

# Dialysis treatment removes urea and other waste products from a patient’s blood by diverting some of the bloodflow externally through a machine called a dialyzer. The rate at which urea is removed from the blood (in mg/min) is often well described by the equation u ( t ) = r V C 0 e − r t / V where r is the rate of flow of blood through the dialyzer (in mL/min), V is the volume of the patient’s blood (in mL), and C 0 is the amount of urea in the blood (in mg) at time t = 0 . Evaluate the integral ∫ 0 ∞ u ( t ) and interpret it.

To determine

To evaluate:

The integral 0u(t) and interpret it.

Explanation

Given:

u(t)=rVC0ert/V

C0-Amount of urea in the blood at t=0

V -Volume of patient’s blood

r -rate of flow of blood through dialysis.

Formula: If a is a positive constant then

0e-atdt=1a

u(t)=rVC0ert/V

0u(t)dt=0rVC0<

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