Step-by-step explanation:
From the statement:
M: is total to be memorized
A(t): the amount memorized.
The key issue is translate this statement as equation "rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized"
memorizing rate is .
the amount that is left to be memorized can be expressed as the total minus the amount memorized, that is .
So we can write
And that would be the differential equation for A(t).