Assignment:
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 60,000 units. That is, the limit as t → ∞ is 60. After 1 year, 5,000 units have been sold (S = 5). Find S as a function of t.
Hint: Use separation of variables in the solution.
Provide complete and step by step solution for the question and show calculations and use formulas.