Final answer:
The equation y=y(3-ty) suggests an inverse relationship between y and t. As t increases, y must decrease to maintain the constant product ty=2, indicating a hyperbolic relationship if graphed.
Step-by-step explanation:
The student's question, 'y=y(3-ty) describe how solutions appear to behave as t increases', can be interpreted as a differential equation where y is a function of t. To analyze how the solutions behave as t increases, let's rewrite the equation in a more standard form: y = y(3 - ty) can be simplified assuming y is not zero (since y=y would be trivial), to 1 = 3 - ty, which further rearranges to ty = 2. This rearranged form tells us that the product of t and y is a constant 2. As t increases, y must decrease reciprocally, since if t goes up, y has to go down to maintain the product at 2. This behavior suggests an inverse relationship between t and y. Graphically, we would observe a hyperbolic shape if we were to plot y against.