Question

given:

dx/dt=kx(N-x)

N=1000
k=1/250
x=2

diff equation for dx/dt:
x(t) = (N e^(c_1 N+k N t))/(e^(c_1 N+k N t)-1)

do i solve for the arbitrary constant?

what is t when N=499?

Answer 1

let me know if my question needs any clarification

Answer 2

Usually they provide a t (0) in the word problem so that you can solve for C.

Answer 3

x is 2 when t(0)

Answer 4

Alright that makes sense all you would have to do is set X(t) = 0 when t = 2 to solve for C. Then use the I.V.P to solve for t when N = 499

Answer 5

so i plug in 1000=N when solving with t=2

Answer 6

i mean 998

Answer 7

Im not sure where you got the 998?

Answer 8

nvm lol

Answer 9

x(t) = (N e^(c_1 N+k N t))/(e^(c_1 N+k N t)-1)

so when setting the t=0 the kNts cancels out

Answer 10

Where are you getting all these crazy differential situations ha ha, I am also taking it and I haven't had a problem until I met your problems.

Answer 11

e^(0) = 1

Answer 12

so C is 0.

well this is for a social diffusion question see how long rumors travel in a pop.

Answer 13

or does c no exist

Answer 14

You should be able to take out C from the exponential function.

Answer 15

Usually when I have something like:\[e^{x+c}= e^x \times e^x = C_1e^x\]

Answer 16

but since x(t)=0 then 0/e^2 ---> c=0

Answer 17

Did you use this method?