Monthly sales of a particular personal computer are expected to decline at the following rate of S′(t) computers per​ month, where t is time in months and​ S(t) is the number of computers sold each month. S′(t)=−20t2/3 The company plans to stop manufacturing this computer when monthly sales reach 500 computers. If monthly sales now ​(t=​0) are 1,580 ​computers, find​ S(t). How long will the company continue to manufacture this​ computer?

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