Consider the following two differential equations that model two students’ rates of memorizing a poem. aly’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
dla/dt = 2(1 - la) and dlb/dt = 3(1 - lb)^2
where la(t) and lb(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 memoriz- ing together having never seen the poem before?
(b) which student has a faster rate of learning at t = 0 if they both start memoriz- ing 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 memoriz- ing together having already learned one-third of the poem?