Answer: equation = dA/dt = K₁ (M - A) - K₂A
Step-by-step explanation:
Let us follow this carefully to get our equation right.
From the question we are told to (Assume the constants of proportionality for the rate at which material is memorized and the rate at which material is forgotten are k1 > 0 and k2 > 0, respectively. Use A for A(t) ).
The Rate of memorizing the material is ∝ [Total amount to be memorized] - [Amount memorized]
remember using A for A(t).
where A rep the amount memorized at a time t and M is the Total amount memorized.
so we have that dA/dt ∝ M - A
which is dA/dt = K₁ (M - A) ---------------(*)
remember it was stated that forgetfulness is taken into account
Forgetfulness, F ∝ A
F = K₂A --------------- (**)
which implies the rate of memorization is decreased as a result of forgetting;
this leads to
dA/dt = K₁ (M - A) - K₂A
The rate of differential equation is ⇒ dA/dt = K₁ (M - A) - K₂A
cheers i hope this helped!!!!
