GreenWealth Incorporated is an investment company whose
nancial

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,

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?

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,

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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