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 $6000 is deposited in a savings account drawing 5 and 3/4% annual interest compounded continuously?

(b) In how many years will the initial sum deposited have doubled? (Round your answer to the nearest year.) (

c) Use a calculator to compare the amount obtained in part (a) with the amount S=6000 (1+1/4(0.0575))^7 that is accrued when interest is compounded quarterly. S= $