An inferior product with a large advertising budget does well when it is introduced, but sales decline as people discontinue use of the product. Suppose that the rate of weekly sales revenue is given by

where S is sales in thousands of dollars and t is time in weeks.
(a) Find the function that describes the weekly sales.
(b) Find the sales for the first week and the ninth week.

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400 S'(t) = (t + 1) 200 (t+ 1)?