logistics and integral calculas

Can somebody please help me with this homework question. I haven’t got much of an idea on what to do!

Infection rate of a disease has a constant of 0.004, this may be represented mathematically by -

**dN/dt = 0.0004N(1000-N), N(0)=1**

1. Using Integral calculus derive a model to determine the number of people with this disease and any time “t”.

2. Use this model to predict how long it will take for 75% of the population will be infected. Population = 1000

3. Discuss the limitations of the model for long term predictions.