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Question 4. Money flows to the new Ponzi scheme at a rate proportional to the square root of the total invested capital, i.e., Ay(t) = √yªt, where y(t) is the total capital invested and t is time. It starts at t = 0 with just $100 of total capital, i.e., y(0) = 100 a) Write down the differential equation for y(t) and specify the initial condition. b) Find y(t) c) The Ponzi scheme bubble will burst when the total investment reaches $1,000,000. When will this happen?

Question 4. Money flows to the new Ponzi scheme at a rate proportional to the square root of the total invested capital, i.e., Ay(t) = √yªt, where y(t) is the total capital invested and t is time. It starts at t = 0 with just $100 of total capital, i.e., y(0) = 100 a) Write down the differential equation for y(t) and specify the initial condition. b) Find y(t) c) The Ponzi scheme bubble will burst when the total investment reaches $1,000,000. When will this happen?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Question 4. Money flows to the new Ponzi scheme at a rate proportional to the square root of the total invested capital, i.e., Ay(t) √yªt, where y(t) is the total capital invested and t is time. It starts at t = 0 with just $100 of total capital, i.e., y(0) = 100 a) Write down the differential equation for y(t) and specify the initial condition. b) Find y(t) c) The Ponzi scheme bubble will burst when the total investment reaches $1,000,000. When will this happen? d) Find the average amount of money invested in this Ponzi scheme during its life (from t=0 until it bursts).
Transcribed Image Text:Question 4. Money flows to the new Ponzi scheme at a rate proportional to the square root of the total invested capital, i.e., Ay(t) √yªt, where y(t) is the total capital invested and t is time. It starts at t = 0 with just $100 of total capital, i.e., y(0) = 100 a) Write down the differential equation for y(t) and specify the initial condition. b) Find y(t) c) The Ponzi scheme bubble will burst when the total investment reaches $1,000,000. When will this happen? d) Find the average amount of money invested in this Ponzi scheme during its life (from t=0 until it bursts).
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