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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 $$c(t)=\frac{K}{V} c_{0} e^{-K_{I} / V}$$ where $K$ is the rate of flow of blood through the dialyzer $(\mathrm{in}$$\mathrm{mL} /\mathrm{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 $\int_{0}^{30} c(t) d t$ and interpret it.

$C_{0}\left(1-e^{-30 r / V}\right)$

Calculus 1 / AB

Calculus 2 / BC

Chapter 5

Integrals

Section 4

The Substitution Rule

Integration Techniques

Oregon State University

Harvey Mudd College

University of Michigan - Ann Arbor

University of Nottingham

Lectures

01:11

In mathematics, integratio…

06:55

In grammar, determiners ar…

0:00

Dialysis treatment removes…

02:42

13:06

Dialysis removes urea from…

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04:21

Dialysis A model that esti…

05:19

Kidney Dialysis Hemodialys…

08:13

2. Hemodialysis is a proce…

02:37

Patients undergo dialysis …

07:59

Dialysis treatment adequac…

So this is our integral. We end up with K divided by V. C zero multiplied by e to the power Negative. Katie divided. Be divided by t over V and we're gonna evaluate this from 0 0 to 30 and that's your final answer.

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