A company incurs debt at a rate of

dollars per year, where t is the amount of time (in years) since the company began. By the fourth year, the company had accumulated $16,260 in debt.
(a) Find the total debt function.
(b) How many years must pass before the total debt exceeds $40,000?

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D'(t) = 90(t + 6)√₁² + 12t