When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t, that is, dS/dt = rS, where r is the annual rate of interest. (a) Find...

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Extracted text: When interest is compounded continuously, the amount of money increases at a rate proportional to the amount S present at time t, that is, dS/dt = rS, where r is the annual rate of interest. (a) Find the amount of money accrued at the end of 5 years when $9000 is deposited in a savings account drawing 5% annual interest compounded continuously. (Round your answer to the nearest cent.) $ 6665.5 X (b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.) 12 years 5(4) that is accrued when interest is compounded (c) Use a calculator to compare the amount obtained in part (a) with the amount S = 9000 ++ quarterly. (Round your answer to the nearest cent.) S = $