2. Let y(t) denote the amount learned at time t (days), in % of the learning task. The following hypotheses are proposed to model the learning task:
HYPOTHESIS I: "The rate of learning is proportional to the amount left to be learned."
HYPOTHESIS II: "The rate of learning is inversely proportional to the amount already learned."
The following data are available:
A learner starts out knowing 20% of the material.
- After 20 days, this learner has mastered 90% of the learning task.
For hypothesis I: "The rate of learning is proportional to the amount left to be learned."
a. Formulate the model as a differential equation (DE)
b. Solve the DE by separating the variables
c. Identify the values of the unknown constants from the data
d. Plot the learning curve in the adjacent figure
fort = 0 to 30 days. Scale the axes of the graph.