Replying to Calc 2 Help for $

So I have this calc 2 take home test due tomorrow and I've finished all but one question and need some help. So to all you calc 2 geniuses out there who want to make $30 for maybe 30 minutes of work help me out.

Suppose a rumor was started on Monday (2 days ago) by a student that my tests are too easy. Today the rumor is known by 1000 students. The rumor spreads at a rate proportional to the product of the number of students who have heard the rumor and those who have not yet heard the rumor. If there are a total of 22,000 students, then

a) give a de that models the spread of the rumor along with initial conditions

b) solve the de and determine how long it will take for half of the student population to hear the rumor

c) how long will it take for all students to hear the rumor.

First person to PM me a photo of all the work with detailed explanations and there paypal address will be $30 richer.