   Chapter 10.4, Problem 9E ### 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

# Medication For Problems 9 and 10, consider that when medicine is administered, reaction (measured in change of blood pressure or temperature) can be modeled by R = m 2 ( c 2 − m 3 ) where c is a positive constant and m is the amount of medicine absorbed into the blood (Source: R. M. Thrall et al., Some Mathematical Models in Biology, U.S. Department of Commerce, 1967).Find the amount of medicine that is being absorbed into the blood when the reaction is maximum.

To determine

To calculate: The amount of medicine absorbed if reaction is maximum.

Explanation

Given Information:

The equation for reaction is given as:

R=m2(c2m3)

Where c is a constant and m is the amount of medicine absorbed in the blood.

Formula used:

To find the maximum value, calculate the relevant stationary value of an equation. Differentiate the function with respect to the independent variable and equate it to 0. the relevant value is the stationary value that satisfies the provided conditions.

The power rule is used for a function in which the expression can be written as every term raised to a power (be it fractional, positive or negative). For the function f(x)=xn, the derivative is

ddx[xn]=nxn1

Calculation:

The equation for reaction is given as

R=m2(c2m3)

Where, c is a constant and m is the amount of medicine absorbed in the blood

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