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 7 years when $9000 is deposited in a savings account drawing 52% annual interest compounded continuously. (Round your answer to the nearest cent. $ 11702 (b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.) 12 years (c) Use a calculator to compare the amount obtained in part (a) with the amount S = 9000 1 + 7(4) that is accrued when interest is compounded quarterly. (Round your answer to the nearest cent.) S = $

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.