In the theory of learning, the rate at which a subject is memorized is assumed to be proportional to the amount that is left to be memorized. suppose m denotes the total amount of a subject to be memorized and a(t) is the amount memorized in time t > 0. determine a differential equation for the amount a(t). (assume the constant of proportionality is k > 0. use a for a(

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).

can you complete your sentence? i could !