A meme is a piece of information that spreads from person to person. For example

Question

A meme is a piece of information that spreads from person to person. For example a meme is used to raise public awareness like "there is a measles outbreak in Disney Land". A telephone company who produces smart phone X might want the meme " Phone X bends in your pocket" to spread as slowly as possible as not get their sales down quickly. If people acquire the meme by any public sources, the rate of acquisition is proportional to the number of people that don't have the meme. Let P denotes the population and let I denotes the number of people who heard the meme. a) Write a differential equation for the number of people who have acquired the meme by time t. b) Solve the differential equation assuming the population we consider is 100,000. c) Sketch the slope field using Maple. d) Sketch solutions corresponding to the initial conditions that nobody (except the mass media) has the meme initially, that 25000people have it initially. If meme is spread by word of mouth, the rate of acquisition is proportional to the product of people who have the meme and number of people who don't. e) Write a differential equation for the number of people who have acquired the meme by time t. a) Use maple to obtain direction field for the differential equation. b) Sketch solutions corresponding to the initial conditions that 1 person has the meme initially, 25000 people have it initially and that nobody has it initially. c) How would your solutions in 1 and 2 change if everybody has it initially?

Explanation / Answer

P= M+N+S

As per the Law of Differentials

N is directly proportional to S^32.

Hence, P~12

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