Report, edit, etc...Posted by CornMuffin on 2007-01-12 at 22:47:00
I need help with my calculus homework...
Here is the problem that I'm stuck on:
The first thing I realised about dy/dt = 2y(1-y) is that it is a logistic equation (ie dP/dt = kP(1-P/D) )
I mostly need help with part a, I can find out rest after that...
Here is the problem that I'm stuck on:
QUOTE
A certain rumor spreads through a community at the rate of dy/dt = 2y(1-y) , where y is the proportion of the population that has heard the rumor at time t.
a. What proportion of the population has heard the rumor when it is spreading the fastest?
b. If at time t = 0 ten percent of the people have heard the rumor, find y as a function of t.
c. At what time t is the rumor spreading the fastest?
a. What proportion of the population has heard the rumor when it is spreading the fastest?
b. If at time t = 0 ten percent of the people have heard the rumor, find y as a function of t.
c. At what time t is the rumor spreading the fastest?
The first thing I realised about dy/dt = 2y(1-y) is that it is a logistic equation (ie dP/dt = kP(1-P/D) )
I mostly need help with part a, I can find out rest after that...
Report, edit, etc...Posted by IsolatedPurity on 2007-01-13 at 03:22:24
Gotta love the internets:
http://mathforum.org/dr.math//problems/maj...a.04.01.99.html
http://mathforum.org/dr.math//problems/maj...a.04.01.99.html
Report, edit, etc...Posted by CornMuffin on 2007-01-13 at 12:42:06
Thanks...i thought it might have been somewhere on the internet lol
Report, edit, etc...Posted by IsolatedPurity on 2007-01-13 at 14:44:18
You just need to know what to google...
"rumor spreads through a community at the rate of dy/dt = 2y(1-y)"
Hopefully you only looked at a's anwser so you could try to do b and c by yourself
.
"rumor spreads through a community at the rate of dy/dt = 2y(1-y)"
Hopefully you only looked at a's anwser so you could try to do b and c by yourself
.