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Question: A drug is administered intravenously at a constant rate of r mg/hour and is excreted at a rate proportional to the quantity present, with constant of proportionality α > 0.
(a) Solve a differential equation for the quantity, Q, in milligrams, of the drug in the body at time t hours. Assume there is no drug in the body initially. Your answer will contain r and α. Graph Q against t. What is Q∞, the limiting long-run value of Q?
(b) What effect does doubling r have on Q∞? What effect does doubling r have on the time to reach half the limiting value, ½ Q∞?
(c) What effect does doubling α have on Q∞? On the time to reach ½ Q∞?
Your task as the nursing home administrator is determine the method for tracking and managing the patient account fund.
A postal service will accept packages only if the length plus girth is no more than 114 inches. Assuming that the front face of the package is square, what is the largest volume package that the postal service will accept?
Express the temperature of the roast 30 minutes after being placed in the oven in function notation and then calculate that value.
Using equations (4) and (5) above and Parseval's Theorem, show that the energy in the string considered above is finite provided that 1 and g are finite energy.
In the morning, may drove to an appointment at 50 miles an hour. Her average speed on the return trip in the afternoon was 40 miles per hour period the return trip took 1/8 hour longer. How far did she travel to the appointment
Write and implement code to do RSA encryption and decryption. Use it to send a message to someone else in the class.
Find (dy/dx) by implicit differentiation for the following equation:
A plane flies 540 miles for 2 hours in the direction of the wind. Then it turns around and flies 690 miles for 3 hours against the same wind. Find the speed of the plane in still air and the wind speed.
a ladder leans against a building that has a wall slanting away from the ladder at an angle of 96 degrees with the ground. if the bottom of the ladder is 23 feet from the base of the wall and it reaches a point 52 feet up the wall,
A piece of wire 46 inches long is bent into the shape of a rectangle having width of x and length of y. Express the area A of the rectangle as a function of x.
What is the probability that seven, eight, or nine parts were produced by machine B?
Write the first 6 terms of each arithmetic sequence. an = an-1 + 6, a1 = -9 and an = an-1 + 4, a1 = -7
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