In order for a movie to become a box office hit, its popularity (as in positive

Question

In order for a movie to become a box office hit, its popularity (as in positive audiences 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 wife release. Else it quickly fades away, relegated to second run theaters. If the films popularity should surpass the threshold level it would become a bona fide hit. Therefore, after production and marking 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 block buster and its ticket sales would sky rocket - sometimes o an enormous level. Until a saturation level (K) when the markets spending capacity is reached. As the marketing director for the motion picture Hannah Montana: the Movie II, you expect, based on extensive marketing researches, that the films popularity can be modeled by the following autonomous equation )in million of ticket- buying "tweens" spending parents money):

p' = -p(2p-24)(3p-63)2(p-50)

A. Identify the values of T, B and K, and classify the stability of their respective equilibrium solution.
B. If p(1065)=5, to what value will p approach eventually?
C.If p(2012)=21.00001 to what value will p approach eventually?

I'm confused how to find T , B and K are they the equilibrium asymptotes ?

Explanation / Answer

set p'=0 find the non-zero values u get T=12 B=21 K=50

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