SOLUTION: An advertising agency begins a campaign to promote a new product and determines that t days later, the number of people N(t) who have heard about the product is changing at a rate

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Question 206134: An advertising agency begins a campaign to promote a new product and determines that t days later, the number of people N(t) who have heard about the product is changing at a rate given by: N'(t) = 5t^2 - (0.04/t^2 3) people per day. How many people learn about the product during the first week? During the second week?

Answer by Marth(57) About Me  (Show Source):
You can put this solution on YOUR website!
N'(t) = 5t%5E2+-+%280.04%2F%28t%5E%282%2F3%29%29%29
So the number of people who have heard about the product can be found by integrating N'(t).
integral(5t%5E2+-+%280.04%2F%28t%5E%282%2F3%29%29%29) = %285%2F3%29t%5E3+-+%280.12t%5E%281%2F3%29%29


The first week encompasses days 0 to 7, so find %285%2F3%29t%5E3+-+%280.12t%5E%281%2F3%29%29from 0 to 7.


For the second week, find %285%2F3%29t%5E3+-+%280.12t%5E%281%2F3%29%29 from 7 to 14.