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GreenWealth Incorporated is an investment company whose nancial assets grow at a continuous rate of 4%. (Pretend the last year or so didnt happen.

GreenWealth Incorporated is an investment company whose …nancial
assets grow at a continuous rate of 4%. (Pretend the last year or so didn’t
happen.) From this must be deducted its expenses–payroll, rent, etc–amounting
to $200 million per year, which we shall assume has to be paid at a steady,
continuous rate.
(a) Let W(t) be the net worth of GreenWealth (that is, assets - expenses)
at time t, where t is measured in years and W in millions of dollars. Derive a
di¤erential equation for W(t).
(b) Find the equilibrium solution Weq of the DE, and interpret it in …nancial
terms.
(c) Find two solution functions W(t), one with initial value greater than
Weq, and one with initial value less than Weq.
(d) Is the equilibrium solution stable?

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