Question

As you know, when a course ends, students start to forget the material they have learned. One model (called the Ebbinghaus model) assumes that the rate at which a student forgets material is proportional to the difference between the material currently remembered and some positive constant, a.

A. Let y=f(t) be the fraction of the original material remembered t weeks after the course has ended. Set up a differential equation for y, using k as any constant of proportionality you may need (let k>0).

Answer 1

Your equation will contain two constants; the constant a (also positive) is less than y for all t.
dy/dt=
B.If after one week the student remembers 80 percent of the material learned in the semester, and after two weeks remembers 70 percent, how much will she or he remember after summer vacation (about 14 weeks)?
percent =

Answer 2

@Zarkon HELP

Answer 3

i got this question

Answer 4

thanks @dumbcow

Answer 5

but i am struck on this one: http://openstudy.com/study#/updates/4f5ad04de4b0602be437a5ec

Answer 6

Assume initial conditions:
y(0) = 1
a is absolute min y, or limit as t-> infinity
so y(t) is a decreasing function, so dy/dt must be negative
given dy/dt is proportional to difference between y and a
\[\frac{dy}{dt} = -k(y-a)\]
rearrange variables
\[\frac{dy}{y-a} = -k dt\]
....
ok great