A 30-year-old woman accepts an engineering position with a starting salary of $30,000 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 ΔA in terms of Δt 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.