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October 2, 2014

October 2, 2014

Posted by **sean** on Wednesday, May 9, 2007 at 7:10pm.

The number, N, of people who have heard a rumor spread by mass media at time, t, in days is modelled by

N (t) = a / 1+ be^ -kt

a. If 50 people have heard the rumour initially and 300,000 people hear the rumour eventually, find a and b

b. If the rumour is initially spreading at the rate of 500 people per day, find k.

Thanks.

for a)

initially ---> t=0

so 50 = a/(1 + be^0)

50 = a/(1+b)

a=50 + 50b ----- (#1)

I will interpret "eventually" to mean t --> ∞

then e^(-large) ---> 0

and 300000=a/(1+0), so a=300000

putting this back in #1 gives b=5999

so N(t) = 300000/(1 + 5999e^-kt)^-1

for b)

N'(t) = -300000((1 + 5999e^-kt)^-2)(e^-kt)(-k)

"initially" the rate is 500 means

500 = -300000(1+5999)^-2 * (1)(-k)

..

..

I got k=10, check my arithmetic please

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