The mathematical model  for proportion is .

(a)

Find the limiting proportion of correct responses as  approaches infinity.

Limiting proportion of correct responses as  approaches infinity.

.

Limiting proportion of correct responses as  approaches infinity is .

(b)

Apply derivative on each side with respect to .

.

.

The rate at which is changing is .

The rate at which is changing when trials is

Substitute in .

.

The rate at which is changing when trials is .

The rate at which is changing when trials is

Substitute in .

.

The rate at which is changing when trials is .

(a) Limiting proportion of correct responses as  approaches infinity is .

(b) The rate at which is changing when trials is .

The rate at wich is changing when trials is .