Explanation Given: The rate at which body eliminates a certain drug (in milliliters per hour) is given by R ( t ) = 60 t ( t + 1 ) 2 ( t + 2 ) , where t is the number of hours since the drug was administered. Calculation: The rate at which body eliminates a certain drug (in milliliters per hour) is given by R ( t ) = 60 t ( t + 1 ) 2 ( t + 2 ) . So, the amount of the drug eliminates during the first hour is the area under the graph of R ( t ) = 60 t ( t + 1 ) 2 ( t + 2 ) from t = 0 to t = 1 . Hence, the amount of drug eliminates during the first hour is, Amount = ∫ 0 1 60 t ( t + 1 ) 2 ( t + 2 ) d t . Choose the change of variable function u = t + 1 , d u = d t . Since, the variable of the integral change form t to u , hence the limits also be changed. Lower limit: If t = 0 then u = 1 . Upper limit: If t = 1 then u = 2 . Substitute t = u − 1 in the above integral and obtain as follows. Amount = 60 ∫ 1 2 ( u − 1 ) ( u ) 2 ( u + 1 ) d u Use partial fraction and rewrite as, Amount = 60 ∫ 1 2 [ − 1 u 2 − 2 u + 1 + 2 u ] d u = 60 [ 1 u − 2 ln ( u + 1 ) + 2 ln u ] | 1 2 = 60 ( 1 2 − 2 ln ( 3 ) + 2 ln ( 2 ) ) − 60 ( 1 1 − 2 ln ( 2 ) + 2 ln ( 1 ) ) = 60 ( − 1 2 + 2 ln ( 2 3 ) + 2 ln 2 ) Simplified further as, Amount = 60 ( − 1 2 + 2 ln ( 4 3 ) ) = 4.522 mL Hence, the amount of drug is eliminated during the first hour after it was administered are 4

Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

13th Edition

ISBN: 9780321869838

Author: Raymond A. Barnett, Michael R. Ziegler, Karl E. Byleen

Publisher: PEARSON

See similar textbooks

Question

Chapter 6, Problem 52RE

To determine

To find: The amount of drug is eliminated during the first hour after it was administered, and during the fourth hour.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 6, Problem 51RE

Chapter 6, Problem 53RE

Students have asked these similar questions

Trolley of the overhead crane moves along the bridge rail. The trolley position is measured from the center of the bridge rail (x = 0) is given by x(t) = 0.5t^3-6t^2+19.5t-14 : 0 <= t <= 3 min. The trolley moves from point A to B in the forward direction, B to C in the reverse direction and C to D again in the forward direction. CONTROL PANEL END TRUCK- RUNWAY BEAM- BRIDGE RAIL HOIST -TROLLEY TROLLEY BUMPER TROLLEY DRIVE LPENDANT TRACK -TROLLEY CONDUCTOR TRACK WIRE ROPE -HOOK BLOCK -BRIDGE DRIVE -END TRUCK BUMPER -RUNWAY RAIL TROLLEY END STOP -CONDUCTOR BAR PENDANT FESTOONING TROLLEY FESTOONING PENDANT CABLE PENDANT x(t)=0.5t^3-6t^2+19.5t-14 v(t)=1.5t^2-12t+19.5 a(t)=(dv(t))/dt=3t-12 Fig. T2.2: The overhead crane Total masses of the trolley, hook block, and the load attached to the hook block are 110 kg, 20 kg, and 150 kg. Damping coefficient, D, is 40 kg/s. What is the total amount of energy required from the trolley motor to move the system [Hint: Use Newton's 2nd law to obtain the…

CONTROL PANEL- BRIDGE RAIL HOIST -TROLLEY TROLLEY BUMPER -BRIDGE DRIVE END TRUCK- RUNWAY BEAM- END TRUCK BUMPER -RUNWAY RAIL TROLLEY DRIVE TROLLEY END STOP -CONDUCTOR BAR LPENDANT TRACK TROLLEY CONDUCTOR TRACK -WIRE ROPE PENDANT FESTOONING TROLLEY FESTOONING -PENDANT CABLE -HOOK BLOCK PENDANT

Find only the residues don't share the same pic as answer else I'll report Find the residue of F(z) = cot z coth z Don't use any Al tool show ur answer in pe n and paper then take z³ at z = 0.

Chapter 6 Solutions

Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)

Ch. 6.1 - Matched Problem 1 Find the area bounded by f(x) =...Ch. 6.1 - Matched Problem 2 Find the area between the graph...Ch. 6.1 - Prob. 3MP Ch. 6.1 - Matched Problem 4Find the area bounded by f(x) =6 ...Ch. 6.1 - Matched Problem 5Find the area bounded by f(x)=2x2...Ch. 6.1 - Matched Problem 6Find the area (to three decimal...Ch. 6.1 - Prob. 7MP Ch. 6.1 - Prob. 1ED Ch. 6.1 - In Problems 18, use geometric formulas to find the...Ch. 6.1 - In Problems 18, use geometric formulas to find the...

Knowledge Booster