The body metabolizes an antibiotic over time (this is why we take it for several days at specified time intervals). Let C'(t) represent the concentration of the antibiotic that remains in the body at time t, where t is measured in hours after the dose has been taken. Assume the rate of change of the concentration is proportional to the concentration left in the body. dC (a) Write a differential equation for Use k as your constant of proportionality. dt dC dt (b) Solve the differential equation given that originally there were approximately 2290 milligrams of the antibiotic in the body, but 3 hours later, the concentration was approximately 1870 mg. C(t) = (c) What is the concentration after 5.5 hours? Round to the nearest whole number. mg (d) When the concentration of antibiotic falls below 1634 mg, the patient will need to take another dose to replenish the amount in the body until the infection is cured. At what time does this occur? Round to two decimal places. hours

Q: Newton's law of cooling says that a hot object cools rapidly when the difference between its…

A:

Q: dT Newton's law of cooling states that the rate of change in the temperature T(t) of a body is…

A: To approximate the temperature of the body using Euler's method, we need to use the formula derived…

Q: It takes a total of 12 hours to drain a tank by opening a valve at the bottom. The depth h (in…

A:

Q: A certain rumor spreads through a community at the rate dy/dt=3y(1+y) , where y is the portion of…

A:

Q: Newton's law of cooling states that the rate of change in the temperature T(t) of a body is…

A: Given Data: Newton's law of cooling states that the rate of change in the temperature​ T(t) of a…

Q: The time variation of the price C of a particular material is described by the equation C = 5t In(t)…

A:

Q: Let a and b be positive numbers. A curve whose equation is y = e -ae bx is called a Gompertz growth…

A:

Q: profit

A:

Q: An accessories company finds that the cost, in dollars, of producing x belts is given by…

A: The cost of producing x belts in dollars is given by the function,

Q: dt' Population growth is commonly modeled upon the simple statement that the popu- lation growth…

A:

Q: A tank contains 200 liters of fluid in which 50 grams of salt is dissolved. Pure water is then…

A:

Q: We first need to find the population as a function of t. We are given the rate of growth, or rate of…

A: