1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Equilibrium Solutions

  1. Sep 15, 2010 #1
    1. Problem:
    In order for a movie to become a box office hit, its popularity (as in positive audience's words-of-mouth, and buzz in the press) must have risen past a certain critical threshold T among viewers and potential viewers, before and during the first week of its nation-wide release. Else it quickly fades away, relegated to second-run theaters ("two-thumbs down..."). If the film's popularity should surpass the threshold level, it will become a bona fide hit. Therefore, after production and marketing expenses, it would return a tidy profit for the production company. However, if its popularity should ever climb further higher and beyond a break-out level, B, the movie would become a true blockbuster and its ticket sale would skyrocket - sometimes to an enormous level. Until a saturation level, K, when the market's spending capacity is reached. As the marketing director for the motion picture High School Musical IV: College Musical, you expect, based on extensive marketing researches, that the film's popularity can be modeled by the following autonomous equation (in million of ticket-buying children spending parents' money):

    p' = -p(2p-12)(3p-48)2(p-43)​

    (a) Identify the values of T, B, and K, and classify the stability of their respective equilibrium solution.

    (b) If p(1066) = 6, to what value will p approach eventually?

    (c) If p(2010) = 16.0000025, to what value will p approach eventually?



    2. Relevant equations:
    equilibrium sollutions occur whenever y' = f(y) = 0




    3. The attempt at a solution:
    T = critical threshold
    B = break-out level
    K = saturation level

    p' = p(2p-12)(3p-48)2(p-43)
    -p=0
    p=0

    2p-12=0
    p=6

    (3p-48)2=0
    p=16

    p-43=0
    p=43
     
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted