graphics – How to use Manipulate with ListLinePlot

I’d like to run Manipulate with 0<r<=4 that preserves the ListLinePlot of the recurrence table given with the colors shown. I’m looking to use the autorun feature in Manipulate to show how the plot varies with 0<r<=4.

(*Logistics Map Model*)
Clear(r, y0, k, NN)
r = 4; y0 = 0.1; NN = 100;
sol = RecurrenceTable({y(k + 1) == r*y(k)*(1 - y(k)), y(0) == y0}, 
   y, {k, 0, NN});
ListLinePlot(sol, PlotRange -> {{0, NN}, {0, 1}}, PlotStyle -> Green, 
 Mesh -> Full, MeshStyle -> Red)