Practice 7 - ir.fuJ-d r d-af~ f-y{p-y) Jt!y) ~ Jdt ~)~ +...

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f Calculus 2 Mike Huff Spring 2009 (8 points) 9. In a model of epidemics, let y(t), in thousands, be the number of infected individuals in the population at time t, in days. If we assume that the infection spreads to all those who are susceptible, one possible solution for yet) is given by the solution of dy = ky( p - y) where k is a positive constant dt which measures the rate of infection and P , in thousands, is the total population in this situation. Find the solution of this differential equation if y(O) = 2. y (t) s: #- of
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Unformatted text preview: ir.fuJ-d r d-af~ f-y{p-y) Jt!y) ~ Jdt ~)~ + p~y)Jt =KtH I[ ~ f j,1\ J y I -11\ I f-Y I = r t-t c 1" /3-1;::: PK.t-+z, e. rr e 3- :::-ce pf. t-f-Y P ,lt pK-t Y ~ f ce f'--ere y-t eye P 'i.:t z: P cePt-t Y-P PK. . t-Cc :;:;:u!u-I-t c,e l' K..I; ?"t-c(./ KI: J-=A-tE yep-'I)-r f-r ::: lip-t ,I/ f _ Y P-7 ~f ~ J 1 p I t( e.:t )(-fl t . 3 :--1+ cc,-PK. .t' y(o) ':-Z. '7 _ f c--Me-Z: t Z: :=. P 2(.:::. P-Z-c:-=-p-2-L...
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