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
![\frac{dA(t)}{dt}=k(M-A(t))](https://tex.z-dn.net/?f=%5Cfrac%7BdA%28t%29%7D%7Bdt%7D%3Dk%28M-A%28t%29%29)
And that would be the differential equation for A(t).
Cross multiply:
30n = 2400. Then n = 80.