Trying to help my daughter with a homework problem (again)
Prob: person trying to remember names of people; meet 100 prople/day; after 7 days remembers 600 out of 700. Assume rate of change in num remembered, dN/dt equals 100 minus amout directly proportional to N. Write diff eq and solve subject to the ic that knows no names at t=0
So far I got:
dN/dt=100-kN .. after integrating i get:
N=(100-Ce^(-kt))/k where C=+-e^(-kc)
Then substitute ic (0,0)and get C=100
To figure out k, I thought of using
600/700=(100-e^(-k*7))/k
but now I can't figure out how to solve for k. Can any one help? Have I done something wrong earlier? Thanks
2007-03-28 15:15:09 · 2 answers · asked by Hector R 1 in Science & Mathematics ➔ Mathematics
I also get N(t) = 100/k (1 - e^(-kt).
N(7) = 600 = 100/k (1 - e^(-7k))
=> e^(-7k) = 6k - 1
You can't solve this analytically, but you can solve it numerically to get k = 0.206059 (6 dp).
2007-03-28 16:28:39 · answer #1 · answered by Scarlet Manuka 7 · 0⤊ 0⤋
i'm extraordinarily efficient you propose e^(5x+7) --- no longer e to the sq. root... besides, chain rule, spinoff of 5x + 7 is 5, so this comes out in the front.. then the spinoff of e is continuously only itself again... really its, 5e^(5x + 7)
2016-12-02 23:10:44 · answer #2 · answered by dismukes 4 · 0⤊ 0⤋