Science:Math Exam Resources/Courses/MATH102/December 2017/Question 07 (b)

MATH102 December 2017
Other MATH102 Exams

Question 07 (b)

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.

(b) For what values of ${\textstyle a}$ does the word fail to catch on and simply disappear from the language? Choose the best answer.

A. ${\textstyle a\leq 2}$

B. ${\textstyle a\leq 1}$

C. ${\textstyle a\leq 0}$

D. ${\textstyle a\geq 1}$

E. ${\textstyle a\geq 2}$

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