Answer
$ 2.9\ sec$ and $ 4.6\ sec$
Work Step by Step
Step 1. Given the model function $y=0.6\ sin\frac{2\pi}{5}x$, at $y=-0.3\ l/s$ exhaled, we have $0.6\ sin\frac{2\pi}{5}x=-0.3$ or $sin\frac{2\pi}{5}x=-0.5$
Step 2. The general solutions for the above equation are $\frac{2\pi}{5}x=2k\pi+\frac{7\pi}{6}$ and $\frac{2\pi}{5}x=2k\pi+\frac{11\pi}{6}$ or $x=5k+\frac{35}{12}$ and $x=5k+\frac{55}{12}$, where $k$ is an integer.
Step 3. Within each breathing cycle of $[0,5)$ seconds, we have $x=\frac{35}{12}\approx2.9\ sec$ and $x=\frac{55}{12}\approx4.6\ sec$
