Use the symbols provided below to sketch the phase line for the differential equation
$$\frac{dP}{dt} = \left(1-\frac{P}{12}\right)^{3}\!\left(\frac{P}{7}-1\right)P^{5} .$$

To place a symbol on the line click a symbol button then click a point on the line.
To remove a symbol from the line click the "delete" button then click the symbol on the line.

Part B)

Use the phase portrait for this differential equation to give a rough sketch of the solution $P(t)$ with initial condition $$P(0)=4$$ on the interval $[0,\infty)$ in the space below.

To sketch the solution, click the "Show/Hide Tangents" button until the red tangents appear. To move a blue endpoint click it with your mouse and hold the mouse button down while you move the point up or down. To change a slope click a red point, hold the mouse button down and move the red point in any direction. Click the "Show/Hide Tangents" again to make the tangents disappear.

Show/Hide Tangents

Part C)

If $P(0)=4$ what happens to $P(t)$ as $t$ gets very large?
$\displaystyle \lim_{t\to\infty}P(t) =$