
Jaden Y.
asked 11/15/22The equation N(t) = 1900/ 1 + 200e−0.625t models the number of people in a school who have heard a rumor after t days.
1 Expert Answer
Raymond B. answered 02/14/23
Math, microeconomics or criminal justice
N(t) = 1900/(1 + 200e^-0.625t)
would mean that at time t=0
N(0) = 1900/(1+200) = 1900/201 = about 9.45 or about 9 or 10 people initially began spreading the rumor
if the school had 1900 people
N(t) = 1900 = 1900/(1+200e^-5t/8)
1 + 200e^-5t/8 = 1
200e^-5t/8 = 0
as t approaches infinity the rumor spreads to the entire school
to find the time all but one person has heard the rumor
set 1899 = 1900/(1+200e^-5t/8)
1899/1900 = 1/(1+200e^-5t/8)
1+ 200e^-5t/8 = 1900/1800
200e^-5t/8 =about 0.0005266
e^-5t/8 = 0.0005266/200 = .000002633
-5t/8 = ln.000002633
t = (-1.6)ln.000002633 = about 20.558
it takes about 21 days for 1899 of the 1900 people to learn of the rumor
then it takes forever for the last guy to find out
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Peter R.
11/15/22