math
posted by sean .
Could u help me with this question.
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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