Hello, I'm currently working on a calculus problem. I am struggling with finding answer and I was wondering if anyone could help me out with how to solve it?

Problem:

A G5 cell phone is released into a test market with 20,000 potential customers. The number of people who have heard of the new phone follows the model

dP/dt = kP(L - P).

a) if 20 people hear of the phone intially (t=0), and 12 weeks later, 500 people have heard of it, find the particular solution, P(t), the number of people who have heard of the phone after t weeks of advertising.

b) When will 70% of the population have heard of the G5 cell phone?

c) When will the number of people who have heard of the phone be increasing the fastest?