Psychologists interested in learning theory study learningcurves.A learning curve is the graph of a function P(t),theperformance of someone learning a skill as a function of thetraining time t.The derivative dP/dt represents the rate atwhich performance improves.(a)When do you think Pincreases most rapidly?Whathappens to dP/dt as t increases?Explain.(b)If Mis the maximum level of performance of which thelearner is capable,explain why the differential equationdP=KM-P)dtk a positive constantis a reasonable model for learning.(c)Make a rough sketch of a possible solution of this differen-tial equation.