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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

`Q`

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

`I(t)`

the amount that has been memorized after

`t`

hours. (4.1) Write down a differential equation for

`l`

, using

`k`

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

`I_(0)`

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

`I_(0)=Q,I_(0)=(Q)/(2)`

, and

`I_(0)=0`

.