consider an elementary model of the learning process: Although human learning is an extr...

consider an elementary model of the learning process: Although human learning is an extremely complicated process, it is possible to build models of certain simple types of memorization. For example, consider a person presented with a list to be studied. The subject is given periodic quizzes to determine exactly how much of the list has been memorized. (The lists are usually things like nonsense syllables, randomly generated three-digit numbers, or entries from tables of integrals.) If we let L (t) be the fraction of the list learned at time t, where L = 0 corresponds to knowing nothing and

Consider the following two differential equations that model two students' rates of memorizing a poem. Jillian's rate is proportional to the amount to be learned with proportionality constant k = 2. Beth's rate is proportional to the square of the amount to be learned with proportionality constant 3. The corresponding differential equations are

where L j (t) and L B (t) are the fractions of the poem learned at time t by Jillian and Beth, respectively. (a) Which student has a faster rate of learning at t = 0 if they both start memorizing together having never seen the poem before?

(b) Which student has a faster rate of learning at t = 0 if they both start memorizing together having already learned one-half of the poem?

(c) Which student has a faster rate of learning at t = 0 if they both start memorizing together having already learned one-third of the poem?