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Differential EquationsHardModels & Qualitative Behavior

Models & Qualitative Behavior · Hard problem

A loan balance BB (in dollars) grows with continuously compounded interest at 6%6\% per year while the borrower repays continuously at 12001200 dollars per year, so B′=0.06B−1200B' = 0.06B - 1200. The balance starts at B(0)=10000B(0) = 10000. After how many years is the loan paid off? Give an exact answer.