Math Help - write the differential....H1N1

ok so im wondering if i set this problem up correctly.

suppose that 8 people carrying the h1n1 flu virus are introduced into a population of 400 people.

im supposed to determine a differential equation for the number of people who have contracted the flu if the rate at which the disease spreads is proportional to the number of people who have the flu and the students who have not yet been exposed.

ok so here is what i have so far..

k= proportion constant
N= total population(400)
X= # of people infected
(N-x)= # of people not infected
X(0)=8

dx/dt= rate at which the disease spreads.

so dx/dt= kX(N-X)

im confused because once i plug in my numbers, my differential doesnt make sense. i think im missing something or doing something wrong.

dx/dt = 8k(400-x)<--?


any help or assistance would be appreciated thanks in advance.

My thought is this: aren't you done with the problem? You were asked to come up with a differential equation for x. You have that, including the initial condition. You were not asked to solve the DE. There's no need to plug in numbers, if all you were asked to exhibit is the DE itself.

its a bad habit of mine, i saw that numbers were given so i thought i was supposed to use them. and this problem, at least in setting it up seemed straight forward. because i got a couple other problems wrong, i figured i got this one wrong as well. i gonna need to keep chugging problems til my confidence is restored. thanks for your help.

Originally Posted by slapmaxwell1

ok so im wondering if i set this problem up correctly.

suppose that 8 people carrying the h1n1 flu virus are introduced into a population of 400 people.

im supposed to determine a differential equation for the number of people who have contracted the flu if the rate at which the disease spreads is proportional to the number of people who have the flu and the students who have not yet been exposed.

ok so here is what i have so far..

k= proportion constant
N= total population(400)
X= # of people infected
(N-x)= # of people not infected
X(0)=8

dx/dt= rate at which the disease spreads.

so dx/dt= kX(N-X)

im confused because once i plug in my numbers, my differential doesnt make sense. i think im missing something or doing something wrong.

dx/dt = 8k(400-x)<--?


any help or assistance would be appreciated thanks in advance.

You have lost an "x" from the last equation (or rather replaced it with the initial condition for some reason) it should be:

dx/dt = k x (400-x), x(0)=8.

CB

thanks Captain! thats where i got confused, i thought that x = 8 and substituted it into the problem. so the answer should be dx/dt = kx(400-x) ?

Originally Posted by slapmaxwell1

thanks Captain! thats where i got confused, i thought that x = 8 and substituted it into the problem. so the answer should be dx/dt = kx(400-x) ?

Yes

CB