Hi please can I have some help with this problem:
An advertising company designs a campaign to introduce a new product to a metropolitan area of population 4 Million people. Let P(t) denote the number of people (in millions) who become aware of the product by time t. Suppose that P increases at a rate proportional to the number of people still unaware of the product. The company determines that no one was aware of the product at the beginning of the campaign, and that 10% of the people were aware of the product after 30 days of advertising. What is the number of people who become aware of the product at time t .
I can not set up the equation...
My problem I think is thie sentence:
Suppose that P increases at a rate proportional to the number of people still unaware of the product
I found something like
dP/dt= k * ( Po- P(t) ) where Po is the original population. But I am not sure