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alexussaniyah
18.11.2019 •
Mathematics
Under certain circumstances, a rumor spreads according to the equation p(t)=1/1+ae−kt where p(t) is the proportion of the population that knows the rumor at time t, and a and k are positive constants. (a) find limt→[infinity]p(t). (b) find the rate of speed of the rumor. (c) how long will it take for 80% of the population to hear the rumor? here, take a=10,k=0.5 with t measured in hours.
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Ответ:
(a)![\lim_{t \to \infty} \frac{1}{1+ae^{-kt}}=1](/tpl/images/0379/7705/9642f.png)
(b)![\frac{d}{dt}\left(\frac{1}{1+ae^{-kt}}\right)=\frac{ake^{-kt}}{\left(1+ae^{-kt}\right)^2}](/tpl/images/0379/7705/65fe7.png)
(c) 80% of the population will have heard the rumor in about 7.4 hrs.
Step-by-step explanation:
We know that a rumor spreads according to the equation
where
is the proportion of the population that knows the rumor at time
, and
and
are positive constants.
(a) To find
you must:
Use this fact,
Apply this identity, to find![\lim _{t\to \infty \:}\left(1)](/tpl/images/0379/7705/99bf6.png)
(b) To find the rate of speed of the rumor you must find the derivative![\frac{dp}{dt}](/tpl/images/0379/7705/ed344.png)
(c) To find the time that will take for 80% of the population to hear the rumor, you must substitute a = 10, k = 0.5, and p(t) = 0.8 into
and solve for t
Ответ:
does not make sensse?
Step-by-step explanation: