Air resistance acting on a falling body can be taken into account by

the approximate relation for the acceleration.
a= dv/dt= g-kv, where k is a constant. A) Derive a formula for the
velocity of the body as a function of time assuming it starts from rest (v=
0 at t=0)
B) Determine an expression for the terminal velocity, which is the
maximum value the velocity reaches

Use the separation of variables integration method.
dv/(g - kv) = dt
Integrate both sides startuing from t=0, when v = 0, and you get
t = (-1/k) [log (g - kv) - log g]
-kt = log (1 - kv/g)
e^-kt = 1 - kv/g
v = (g/k) (1 - e^-kt)

When t becomes very large, v -> g/k

you suck.

I also didn't ask this. Again, somebody else did this.

Thank you for your feedback. I apologize if there was any confusion or frustration caused. Is there anything specific that I can help you with regarding the explanation of the formula for the velocity of the falling body or the expression for the terminal velocity?