Modeling Population Growth

So I have an equation to describe population growth

where a and b are constants. Typically b is small so that initially, since the population p(t) is small, the squared term can be neglected and the population growth is exponential.

how do I solve the differential equation for p(t) with p(t = 0) = 1 where a = 2 and b = 0.05
and how do I find the value of p(t) as t → ∞

Clear[p]
p[t_] = p[t] /. 
  DSolve[{p'[t] == 2 p[t] - 0.05 p[t]^2, p[0] == 1}, p, t][[1]]
Plot[p[t], {t, 0, 5}]