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?

-kt F(t) = B + (1 - B)e