(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.

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

15th Edition

ISBN: 9781323047620

Author: Barnett, Ziegler, Byleen

Publisher: Pearson Education

See similar textbooks

Concept explainers

Minimization

In mathematics, traditional optimization problems are typically expressed in terms of minimization. When we talk about minimizing or maximizing a function, we refer to the maximum and minimum possible values of that function. This can be expressed in ter…

Maxima and Minima

The extreme points of a function are the maximum and the minimum points of the function. A maximum is attained when the function takes the maximum value and a minimum is attained when the function takes the minimum value.

Derivatives

A derivative means a change. Geometrically it can be represented as a line with some steepness. Imagine climbing a mountain which is very steep and 500 meters high. Is it easier to climb? Definitely not! Suppose walking on the road for 500 meters. Which …

Concavity

In calculus, concavity is a descriptor of mathematics that tells about the shape of the graph. It is the parameter that helps to estimate the maximum and minimum value of any of the functions and the concave nature using the graphical method. We use the …

Videos

Question

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.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11, Problem 45RE

Chapter 11, Problem 47RE

Students have asked these similar questions

Question The function f(x) is shown in the graph below. Which of the following statements are true? Select all that apply. f(x) 12 10 -16 -14 -12 -10 -8 + -4 " 10 12 14 16 a Select all that apply: ☐ Condition 1 is satisfied. ☐ Condition 2 is satisfied. ☐ Condition 3 is satisfied. ☐ f(x) is continuous.

Two planes are flying at the same altitude. One airplane is 60 miles due north of the control tower.Another airplane is located 70 miles from the tower at a heading of 80° east of south. To thenearest tenth of a mile, how far apart are the two airplanes?

Solve it correctly and in French

Chapter 11 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences - Boston U.

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

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.

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

Solution Summary: The author calculates the total amount of the drug that is eliminated from the body.