(Solved): Question 4: 20 Marks In one theory of learning, the rate at which a course is memorized is assumed t ...

Question 4: 20 Marks In one theory of learning, the rate at which a course is memorized is assumed to be proportional to the product of the amount already memorized and the amount that is still left to be memorized. Assume that

denotes the total amount of content that has to be memorized, and

the amount that has been memorized after

hours. (4.1) Write down a differential equation for

, using

for the constant of proportionality. Also, write down the initial value

. (4.2) Draw the phase line of the model. (4.3) Use the phase line to sketch solution curves when the initial values are

, and

.