An isolated college has a student population of 750. One student returns to college unwittingly carrying a 'flu virus. The rate at which the virus spreads is proportional to both the number of students, x, who have so far caught the virus and the number of students still unaffected. The situation can be represented by the differential equation dx/dt = kx(750 - x) where k is the proportional constant.
1) Find the general solution to this differential equation?
2) If the initial conditions are that, when t = 0 then x = 1, find the corresponding integration constant?
3) Given after 4 days (t=4), 25 students are suffereing from the virus, find a value for k and calculate the number of studetns who are suffering by the end of the first week?