A virus spreads at rate proportional to number of people who have contracted the virus and number who have not. let p(t) denote the number of people who contracted virus after t weeks.

a. Suppose there are 18000 people and 1000 contracted the virus at the beginning of first week of the outbreak. Write the initial value problem that models the spread of the virus.

For this one i got this far - dy/dt = ay(p-y) and then take the integral of both sides?..

b. If 2000 people contracted the flue by the end of the first week show that p(t) = 18000/(17((8/17)^t)+1)

And for this im guessing you just plug in 1 for t and make sure its = 2000?

Prefer a written answer and then placed as attachment if possible

Thanks a lot!