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A 30 year old woman accepts an engineering position with a starting salary of $30000 per year. Her salary S(t) increases exponentially with S(t)=30e^(t/20) thousand dollars after t years. Meanwhile 12% of her salary is deposited continuously in a retirement account which accumulates interest at a continuous annual rate of 6%. a) Estimate change(A) in terms of change(t) to derive the differential equation satisfied by the amount A(t) in her retirement account after t years. b) Compute A(40), the amount available for her retirement at age 70.