a. Explanation Given: It is given that a dose D is injected every Thours , and it is seen that the concentration of insulin in a patient’s system decays exponentially and so it can be written as D e − a t , where t represents time in hours and a is a positive constant. Concept Used: In this we have to use the concept of limits and sequence. We use the formula of b n = r n a + c ( 1 − r n 1 − r ) Calculation: If a solution with concentration x units/ per volume of a substance in it is mixes with another solution with concentration y units/per volume of the same substance then the resulting solution has concentration x + y 2 units/per volume. When the first dose D of insulin is injected in the patient’s body the concentration of the insulin in his body after t hours is D e − a t Where a is a positive constant. The dose D of insulin is injected every Thour . So,the concentration of insulin just before the second dose is D e − a T When the dose D is added then the concentration becomes 1 2 ( D + D e − a T ) So the concentration of insulin just before the third dose is 1 2 ( D + D e − a T ) e − a T = D 2 ( 1 + e − a T ) e − a T So if we let C n be the concentration of insulin in the patient’s body just before the (n + 1 )-th dose then we have C n + 1 = ( D + C n 2 ) e − a T With C 0 = 0 Writing in a more simplified way we have C n + 1 = D 2 e a T + ( 1 2 e a T ) C n The solution b. To determine Calculate the limiting pre-injection concentration. c. To determine Find a minimal dosage D in terms of C , a and T ,if the concentration of insulin must always remain at or above a critical value C.

15th Edition

ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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Question

Chapter 2.1, Problem 38E

To determine

Find the expression for the sum of the residual concentration just before the (n+1)
st injection , if

To determine

Calculate the limiting pre-injection concentration.

To determine

Find a minimal dosage D in terms of C , a and T ,if the concentration of insulin must always remain at or above a critical value C.

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Chapter 2.1, Problem 37E

Chapter 2.1, Problem 39E

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Chapter 2 Solutions

BIOCALCULUS:CALCULUS F/LIFE...-W/ACCESS

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Ch. 2.1 - Prob. 11E Ch. 2.1 - Prob. 12E Ch. 2.1 - Prob. 13E Ch. 2.1 - Prob. 14E Ch. 2.1 - Prob. 15E Ch. 2.1 - Prob. 16E Ch. 2.1 - Prob. 17E Ch. 2.1 - Prob. 18E Ch. 2.1 - Prob. 19E Ch. 2.1 - Prob. 20E Ch. 2.1 - Prob. 21E Ch. 2.1 - Prob. 22E Ch. 2.1 - Prob. 23E Ch. 2.1 - Prob. 24E Ch. 2.1 - Prob. 25E Ch. 2.1 - Prob. 26E Ch. 2.1 - Prob. 27E Ch. 2.1 - Prob. 28E Ch. 2.1 - Prob. 29E Ch. 2.1 - Prob. 30E Ch. 2.1 - Prob. 31E Ch. 2.1 - Prob. 32E Ch. 2.1 - Prob. 33E Ch. 2.1 - Prob. 34E Ch. 2.1 - Prob. 35E Ch. 2.1 - Prob. 36E Ch. 2.1 - Prob. 37E Ch. 2.1 - Prob. 38E Ch. 2.1 - Prob. 39E Ch. 2.1 - Prob. 40E Ch. 2.1 - Prob. 41E Ch. 2.1 - Prob. 42E Ch. 2.1 - Prob. 43E Ch. 2.1 - Prob. 44E Ch. 2.1 - Prob. 45E Ch. 2.1 - Prob. 46E Ch. 2.1 - Prob. 47E Ch. 2.1 - Prob. 48E Ch. 2.1 - Prob. 49E Ch. 2.1 - Prob. 50E Ch. 2.1 - Prob. 51E Ch. 2.1 - Prob. 52E Ch. 2.1 - Prob. 53E Ch. 2.1 - Prob. 54E Ch. 2.1 - Prob. 55E Ch. 2.1 - Prob. 56E Ch. 2.1 - Prob. 57E Ch. 2.1 - Prob. 58E Ch. 2.1 - Prob. 59E Ch. 2.1 - Prob. 60E Ch. 2.1 - 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Find the expression for the sum of the residual concentration just before the ( n + 1 ) st injection , if

Solution Summary: The author explains that the concentration of insulin in a patient's system decays exponentially.

Concept explainers

Videos

Find the expression for the sum of the residual concentration just before the (n+1)
st injection , if

Calculate the limiting pre-injection concentration.

Find a minimal dosage D in terms of C , a and T ,if the concentration of insulin must always remain at or above a critical value C.

Want to see the full answer?

Chapter 2 Solutions

Find the expression for the sum of the residual concentration just before the ( n + 1 ) st injection , if

Solution Summary: The author explains that the concentration of insulin in a patient's system decays exponentially.

Concept explainers

Videos

Find the expression for the sum of the residual concentration just before the (n+1) st injection , if

Calculate the limiting pre-injection concentration.

Find a minimal dosage D in terms of C , a and T ,if the concentration of insulin must always remain at or above a critical value C.

Want to see the full answer?

Chapter 2 Solutions

Find the expression for the sum of the residual concentration just before the (n+1)
st injection , if