It is given that dP/dt = rP (r being the annually compounded interest rate and P is the amount in the account at any given time). Suppose that an account earns at an annual rate of r percent...

It is given that dP/dt = rP (r being the annually compounded interest rate and P is the amount in the account at any given time).

Suppose that an account earns at an annual rate of r percent compounded continuously and a person is drawing an income of H dollars per year withdrawn continuously (impossible, but a modeling assumption). Use
phase line analysis
to analyze the behavior of the account. Discuss the meaning of any equilibrium points and their stability. If r = 10% (a reasonable rate for long-term stock investments), and H = $10,000, how long should an initial investment of $50,000 be left untouched so that when withdrawals begin the capital is not depleted?