   Chapter 9.2, Problem 44E ### 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

# Response to adrenalin Experimental evidence suggests that the response y of the body to the concentration x of injected adrenalin is given by y = x a + b x where a and b are experimental constants.(a) Is this function continuous for all x?(b) On the basis of your conclusion in part (a) and the fact that in the context of the application x ≥   0  and  y ≥   0 , must a and b both be positive, both be negative, or have opposite signs?

(a)

To determine

Whether the function, y=xa+bx, is continuous for all values of x, where x is the concentration of injected adrenalin if the experimental evidence shows that the response of the body to the concentration of drugs injected in the body

Explanation

Given Information:

The function, y=xa+bx, where a and b are experimental constants.

Explanation:

Consider the provided function,

y=xa+bx

Since, the function is a rational function, thus, the function will be continuous at all points except the points where the value of the denominator is zero.

Thus, the point of discontinuity is found by equating the denominator to zero

(b)

To determine

The value of a and b, for the concentration of x in the blood to be positive and the answer to part (a) holds true the experimental evidence shows that the response of the body to the concentration of drugs injected in the body.

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