Math Insight

Quiz 9

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Total points: 8
  1. Consider the dynamical system \begin{align*} \diff{ y }{t} &= f(y)\\ y(0) & = y_0, \end{align*} where the function $f$ is graphed below and $y_0$ is an initial condition.

    For each of the below initial conditions, use the following applet to graph of the solution $y(t)$. For each initial condition, enable the corresponding curve and select the correct option for how the speed of the solution changes (either “speed up,” “speed up, then slow down,” or “slow down”). Then, drag the points on the curve so that the solution begins and ends at the correct values. (If the solution is a constant, selecting “slow down” will work.)

    Feedback from applet
    Final value:
    Initial conditions:
    Speed profile:

    Warning (confusing applet behavior): when dragging a point with the mouse, be sure to let go of the mouse button before the pointer moves outside the applet. If not, the point will move again when the mouse pointer returns to the applet.

    1. $y_0 = -9$. (Use the green curve, marked with an A.)
    2. $y_0 = -4$. (Use the blue curve, marked with an B. Click the corresponding diamond to reveal the blue curve.)
    3. $y_0 = -2$. (Use the red curve, marked with an C. Click the corresponding diamond to reveal the red curve.)

  2. What is the solution to the following dynamical system? \begin{align*} v'(t) &= -7.4 v\\ v(0) &= -4.3 \end{align*} $v(t) =$