Science:Math Exam Resources/Courses/MATH102/December 2012/Question C 04 (c)/Solution 1

We want to sketch the solution without solving the equation. Hence, we draw the phase space for $\displaystyle {}Q$ (the number of leaves) and $\displaystyle {}{\textrm {d}}Q/{\textrm {d}}t$ (the daily rate of change of leaves). Therefore, we first make a table with $\ Q$ and the corresponding $\displaystyle {}dQ/dt$.

$\ Q=0$	$\ Q=2$	$\ Q=4$	$\ Q=6$	$\ Q=8$	$\ Q=10$
$\ dQ/dt=5$	$\ dQ/dt=4$	$\ dQ/dt=3$	$\ dQ/dt=2$	$\ dQ/dt=1$	$\ dQ/dt=0$

After drawing the phase space, the curve of the solution can be plotted by following the slopes.