math question, help

[UncleWai]

i have a logistic differential equation dp/dt = 0.002P (1-P/800), it is the rate of the spread of a flu. The question is how many days it take until the maximum number of students are infected. I know it will never reach the carrying capacity, so how do i find when it will reach the maximum number? maximum being..?

 

[AUMM]

mmmm, i beleive you set that equal to zero and solve which would give you the max and min?

 

[alee25]

ya you just set it to zero and find the critical numbers (meaning what values of p will have a rate of 0)

see remember that if there is a function f(x), the derivitive can show on what values f(x) is increasing/decreasing, and the double derivitive (f double prime) shows the concavity...

so basically since rate is the derivitive of the position function (or in this case the number of students that have the flu), find the critical numbers and then see it they are a maximum or minimum (or remember in calc, in order to prove whterh its a max or min, you use this thing: hope this looks ok when posted

I + I - I
I-------------I----------------I
I I I

where on top of each I there is a crit number

edit nevermind, it doesnt look right when posted

 

[b0mbrman]

You can't find the max number with that equation because you don't know how many people had it on day 0 :Q