(A) Explanation Definition used: Improper integral : “If f is continuous on [ a , ∞ ) , then ∫ a ∞ f ( x ) d x = lim b → ∞ ∫ a b f ( x ) d x . If it exists and finite, then it converges otherwise diverges”. Theorem used: Fundamental Theorem : “Let f be a continuous function on [ a , b ] . If F is anti-derivative of f on [ a , b ] , then ∫ a b f ( x ) d x = F ( b ) − F ( a ) ”. Calculation: The rate of elimination of the drug is given by, R ( t ) = 15 e ( − 0.2 t ) − 15 e ( − 0.3 t ) . Integrate R ( t ) = 15 e ( − 0.2 t ) − 15 e ( − 0.3 t ) over the interval [ 0 , ∞ ) to compute the total amount of eliminated drug. Total amount = ∫ 0 ∞ ( 15 e ( − 0.2 t ) − 15 e ( − 0.3 t ) ) d t = 15 lim T → ∞ ∫ 0 T ( e ( − 0.2 t ) − e ( − 0.3 t ) ) d t = 15 lim T → ∞ ( − e ( − 0.2 t ) 0.2 + e ( − 0.3 t ) 0.3 ) | 0 T = − 15 lim T → ∞ ( e ( − 0.2 t ) 0.2 − e ( − 0 (B) To determine To find: The time for which the eliminated drug is 50% of the total amount.

Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)

14th Edition

ISBN: 9780137400126

Author: Raymond Barnett, Michael Ziegler

Publisher: PEARSON+

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Chapter 11, Problem 46RE

(A)

To determine

To find: The total amount of the drug that is eliminated from the body.

(B)

To determine

To find: The time for which the eliminated drug is 50% of the total amount.

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Chapter 11, Problem 45RE

Chapter 11, Problem 47RE

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Chapter 11 Solutions

Pearson eText for Calculus for Business, Economics, Life Sciences, and Social Sciences, Brief Version -- Instant Access (Pearson+)

Ch. 11.1 - Evaluate the following, if it converges: 3dx(x1)2.Ch. 11.1 - Prob. 2MP Ch. 11.1 - Prob. 3MP Ch. 11.1 - Prob. 4MP Ch. 11.1 - Prob. 5MP Ch. 11.1 - Prob. 6MP Ch. 11.1 - Prob. 1ED Ch. 11.1 - Prob. 2ED Ch. 11.1 - Prob. 1E Ch. 11.1 - Prob. 2E

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The total amount of the drug that is eliminated from the body.