# Math Insight

### Quiz 9

Name:
Group members:
Section:
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, increase $n_c$ by one, and move the points to specify the curves position, and click the curve to change it shape. (The shape indicates whether the solutions always speeds up, speeds up then slows down, or always slows down.)

Feedback from applet
Final values of curves:
Initial conditions of curves:
Speed profiles of curves:
1. $y_0 = -9$
2. $y_0 = -4$
3. $y_0 = -2$

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