Consider the following two differential equations that

Chapter , Problem 15

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Consider the following two differential equations that model two students rates of memorizing a poem. Alys rate is proportional to the amount to be learned with proportionality constant k = 2. Beths rate is proportional to the square of the amount to be learned with proportionality constant 3. The corresponding differential equations are d L A dt = 2(1 L A) and d L B dt = 3(1 L B) 2, where L A(t) and L B(t) are the fractions of the poem learned at time t by Aly 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?