Chapter 3, Section 3.5, Question 40 The function 110e e* + e can be used to repr

Question

Chapter 3, Section 3.5, Question 40 The function 110e e* + e can be used to represent the percent of patients exhibiting an above normal temperature response to dose * millimoles (mM) of a particular histamine. Enter the exact answers a. What is the elasticity of R with respect to changes in X 7 b. If there is a 4% error in estimating the dose X when -3 (mh), then what is the percent error in calculating the response R ? The error is Click if you would like to Show Work for this question: Open Show Work LINK TO TEXT

Explanation / Answer

a) Elasitcity of R(x) with respect to x is given by :
E = (dR/dx)*x/R(x)

R(x) = 110ex/(ex + e-3)

dR/dx = 110[(ex+e-3)ex - ex(ex)]/(ex+e-3)2 = 110(ex)*e-3/(ex+e-3)2

E = 110(ex)*e-3/(ex+e-3)2 * x(ex+e-3)/110ex = xe-3/(ex+e-3)

(b) dR/dx =  110(ex)*e-3/(ex+e-3)2

dx/x = 4/100 given x = -3 mm . We need dR/R *100

dR/R = e-3/(ex+e-3) dx

=> dR/R =  e-3/(ex+e-3) * 4x/100

=> dR/R *100 = e-3/(ex+e-3) * 4x

At x=-3 mm

dR/R *100 = e-3/(e-3+e-3) *4(-3)

=> dR/R *100 = e-3/2e-3 *-12 = -12/2 = -6

Hence the error is -6%

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