dy/dx = y(1-y) [this is called the logistic equation, it is used to model the spread of disease, rumors, etc, where x = time and y = # people] ... use step size x=0.05 a) For initial condition (0,3) ... as x gets very big, what happens to the y-value? b) For initial condition (0,2) ... as x gets very big, what happens to the y-value? c) For initial condition (0,0.5) ... as x gets very big, what happens to the y-value? d) For initial condition (0,-0.7) ... as x gets very big, what happens to the y-value? Drag the initial point A around, to see many different possibilities. e) Can you make a prediction for the y-value (at large x-values) based on the initial condition?