According to the Ebbinghaus model (recall Exercise 60, Section 4.1), the fraction F(t) of subject matter you
Question:
According to the Ebbinghaus model (recall Exercise 60, Section 4.1), the fraction F(t) of subject matter you will remember from this course t months after the final exam can be estimated by the formula F(t) = B + (1 − B)e−kt, where B is the fraction of the material you will never forget and k is a constant that depends on the quality of your memory.
a. Find F'(t), and explain what this derivative represents.
b. Show that F'(t) is proportional to F − B, and interpret this result.
c. Sketch the graph of F(t) for the case where B = 0.3 and k = 0.2.
Data from Exercises 60 Section 4.1
According to the Ebbinghaus model, the fraction F(t) of subject matter you will remember from this course t months after the final exam can be estimated by the formula
where B is the fraction of the material you will never forget and k is a constant that depends on the quality of your memory. Suppose you are tested and it is found that B = 0.3 and k = 0.2. What fraction of the material will you remember 1 month after the class ends? What fraction will you remember after 1 year?
Step by Step Answer:
Calculus For Business, Economics And The Social And Life Sciences
ISBN: 9780073532387
11th Brief Edition
Authors: Laurence Hoffmann, Gerald Bradley, David Sobecki, Michael Price