   Chapter 9.8, Problem 37E ### 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

# Sensitivity 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). The sensitivity to the medication is defined to be the rate of change of reaction R with respect to the amount of medicine m absorbed in the blood.(a) Find the sensitivity.(b) Find the instantaneous rate of change of sensitivity with respect to the amount of medicine absorbed in the blood.(c) Which order derivative of reaction gives the rate of change of sensitivity?

(a)

To determine

To calculate: The sensitivity of the reaction R=m2(c2m3).

Explanation

Given information:

The provided reaction R=m2(c2m3) where c is a positive constant and m is the amount of medicine absorb in the blood.

Formula used:

The power rule for differentiation states that,

ddx(xk)=kxk1

The derivative of a constant times a function is

ddx[cf(x)]=cddx(f(x))

The derivative of a sum/difference of terms in a function,

ddx(f±g)=ddxf±ddxg

And sensitivity is the rate of change of reaction with respect to the amount of medicine absorb in the blood.

Thus, Sensitivity =dRdm

(b)

To determine

To calculate: The instantaneous rate of change of sensitivity with respect to the amount of medicine in the blood.

(c)

To determine

The order of derivative involves in the rate of change of sensitivity.

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