For the differential equation $\frac { d y } { d x } = 2 y ( 1 - y )$:

1. What type of growth is described by this equation? Finish the sentence, "The rate of growth is proportional to…"

   Hint (a):

   ... the product of ___ and ___.

2. Solve the differential equation with initial condition $y(0) = 0.5$, and sketch the solution curve.

   Hint (b):

   By partial fraction decomposition:
   Solve for the value of $A$: