Suppose two students are memorizing the elements on a list according to the rate of change equation: dL/dt = 0.5(1-L). L represents the fraction of the list that is memorized at any time t. (a) If one of the students knows one-third of the list at time t = 0 and the other student knows none of the list, which student is learning most rapidly at this instant? Why? (b) What does the rate of change equation predict for someone who begins with the list completely memorized? Explain.

We have a large tank filled with 50 liters of pure water. there is a salt solution of concentration 20 g/L flowing into the tank at a rate of 2 L/min. The well mixed solution is flowing out of the tank at a rate of 1 L/min. find the concentration  of salt in the tank as a function of time. no need to worry about the tank overflowing.

What would the derivative of this look like on a graph?

When drugs are administered into the bloodstream, the amount of the drug present decreases continuously at a constant rate. The amount of a certain drug, Xanaz, in the bloodstream is modeled by the function, where is the initial dosage, and t is the time (in hours) after the initial dose was given. The following chart shows the relationship between the original dose and how much is sti in the system after so much time. Xanax (3mg) amount still in system after X hours 2.5 1.5 0.5 2 10 12 14 16 18 20 22 24 Number of hours after dose was taken After how many hours will there be approximately 1/2 of the original dose in the body? 3. 2. 1. Amount still in the system in mg's