When you changed the coefficient in the 1st equation, the graph did not seem to change. The main difference was in the numbers on the ordinate. Maple autoscales its graphs, and this can give almost the same shape for a graph. Changing the numbers in the plot line has a much more noticable change. If you specify a large interval for the time axis, the plot may blow up because the concentration of organisms goes beyong the number range for your computer.
Unlimited growth makes no sense.
Nutrients would be exhausted and growth would stop. See the Monod equation and the comments about growth-limiting nutrient.