   Chapter 9.6, Problem 52E ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042

#### Solutions

Chapter
Section ### Mathematical Applications for the ...

11th Edition
Ronald J. Harshbarger + 1 other
ISBN: 9781305108042
Textbook Problem

# Concentration of body substances The concentration C of a substance in the body depends on the quantity of the substance Q and the volume V through which it is distributed. For a static substance, this is given by C = Q V For a situation like that in the kidneys, where the fluids are moving, the concentration is the ratio of the rate of change of quantity with respect to time and the rate of change of volume with respect to time.(a) Formulate the equation for concentration of a moving substance.(b) Show that this is equal to the rate of change of quantity with respect to volume.

(a)

To determine

The equation for concentration of a moving substance for function C=QV. If concentration C, quantity of the substance Q and the volume V.

Explanation

Given Information:

The concentration C of a matter depended on the quantity of the matter presents Q and the volume of matter V. For a static substance, this is given by C=QV.

For a situation like that in the kidneys, where the fluids are moving, the concentration is the ratio of the rate of change of quantity with respect to time and the rate of change of volume with respect to time.

Calculation:

Consider the provided function,

C=QV

Where, the concentration C of a matter depended on the quantity of the matter presents Q and the volume of matter V. For a static substance, this is given by C=QV.

The concentration is the ratio of the rate of change of quantity with respect to time and the rate of change of volume with respect to time where the fluids are moving

(b)

To determine

To prove: The equation for concentration of a moving substance is equal to the rate of change of quantity with respect to volume.

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