GreenWealth Incorporated is an investment company whose
assets grow at a continuous rate of 4%. (Pretend the last year or so didnt
happen.) From this must be deducted its expensespayroll, rent, etcamounting
to $200 million per year, which we shall assume has to be paid at a steady,
(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
(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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