Consider the following two differential equations that model two students\' rate
ID: 1947978 • Letter: C
Question
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. Which student has a faster rate of learning at t = 0 if they both start memorizing together having never seen the poem before? 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? 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?Explanation / Answer
a) At t=0, assuming both have never studied the poem before, La=0=Lb Aly's rate of learning = 2*(1-0) = 2 (from the equation) Beth's RoL = 3*(1-0)^2 = 3. b) La = Lb = 1/2 Aly's RoL = 1 Beth's RoL = 3/4 c) La=Lb=1/3 Aly's RoL = 4/3 Beth's RoL = 4/3