Question 4 (5 points). Money flows to the new Ponzi scheme at a rate proportional to the square

root of the total invested capital, i.e., () = , where () is the total capital invested and

is time. It starts at = 0 with just $100 of total capital, i.e., (0) = 100

a) (1 point) Write down the differential equation for () and specify the initial condition.

b) (2 points) Find y(t)

c) (1 point) The Ponzi scheme bubble will burst when the total investment will reach

$1,000,000. When will this happen?

d) (1 point) Find the average amount of money invested in this Ponzi scheme during its life

(from t=0 until it bursts).

Question 4 (5 points). Money flows to the new Ponzi scheme at a rate proportional to the square root of the total invested capital, i.e., y(t)=yt, 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) (1 point) Write down the differential equation for y(t) and specify the initial condition. b) (2 points) Find y(t) c) (1 point) The Ponzi scheme bubble will burst when the total investment will reach $1,000,000. When will this happen? d) (1 point) Find the average amount of money invested in this Ponzi scheme during its life (from t=0 until it bursts)