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Rate of increase function

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SALES: The rate of increase in sales S (in thousands of units) of a product is proportional to the current level of sales and inversely proportional to the square of the time t. This is described by the differential equation:

dS / dt = kS / t^2

where t is the time in years. The saturation point for the market is 50,000 units. That is, the limit as t approaches infinity is 50. After 1 year, 10,000 units have been sold. Find S as a function of t.

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This provides an example of working with rate of increase as a function.

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