MATH102 December 2017
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Question 07 (a)

New words are constantly being introduced into a language. The usage of one particular new word is thought to grow according to a logistic equation

${\displaystyle u'=2u(1-u)-au}$
where ${\textstyle u}$ is the fraction of the population using the word. The usage increases at a rate proportional to the product of the fraction of people who use the word and the fraction that don’t use it and decreases at a rate proportional to the number of users.

(a) The parameter ${\textstyle a}$ represents...

A. ...how appealing the word is when you first hear it (larger ${\textstyle a}$ means more appealing).

B. ...how easy the word is to remember once you start using it (larger ${\textstyle a}$ means easier to remember).

C. ...how easy the word is to forget once you start using it (larger ${\textstyle a}$ means easier to forget).

D. ...how annoyed people that don’t use the word get when they hear it (larger ${\textstyle a}$ means more annoyed).

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