One model for the spread of a rumor is that the rate of spread is proportional to the product of the function y of the population who have heard the rumor and the fraction who have not heard the rumor.
a) write a differential eq. that is satisfied by y.
b) solve the differential eq.
c) A small town has 1000 inhabitants. At 8am, 80 people have heard a rumor. By noon half the town has heard it. At what time will 90% of the population have heard the rumor?
show work/steps plz..thanks!
2007-12-06 15:12:30 · 2 answers · asked by Anonymous in Science & Mathematics ➔ Mathematics
y' = C * (y/N) * (1-y)/N = D y(1-y), where C is the proportionality constant, N is the number of people in the town, and D is C/N^2.
Well, that's a separable differential equation.
dy/(y(1-y)) = D * dx
The LHS equals dy * ( 1/y + 1/(1-y))
You should be able to take it from there! (Hint: Logarithms are your friend.)
2007-12-06 17:52:38 · answer #1 · answered by Curt Monash 7 · 0⤊ 0⤋
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2016-11-13 22:41:23 · answer #2 · answered by ? 4 · 0⤊ 0⤋