A 30-ycar-old woman accepts an engineering position with a starting salary of $30,000 per year. Her salary S(t) increases exponentially, with S(t) − 30et/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 Aft) in her retirement account after t years.
(b) Compute A(40), the amount available for her retirement at age 70.
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