A manufacturer expects to sell a product to 150 000 potential customers. The manufacturer knows that sales will be determined not only by advertising but by how many customers are already using the product and how many are not. Marketing surveys suggest that the rate of customers attracted to the product is governed by the differential equation,
dy/dt=0.004y(150-y)
where y is measured in thousands and t in months. The manufacturer initially gives away 250 copies. How may months does it take for the company to sell products to 90% of the anticipated market?
so I think y here represents the number of customers attracted( thousands of them), and given y(0)=250, they ask for t where y(t)=0.9*150 000? Maybe I'm having a brain block due to sleep deprivation-- not so sure what do do from here, integrate the differential equation? How do I do it?
Any help would be appreciated!