Monthly sales of a particular personal computer are expected to increase at the rate of

S′(t) = -4te^0.1t

computers per month, where t is time in months and S(t) is the number of computers sold each month. The company plans to stop manufacturing this computer when monthly sales reach 800 computers. If monthly sales now (t = 0) are 2,000 computers, find S(t). How long, to the nearest month, will the company continue to manufacture the computer?