Exercise 1.1.29

Question

A homeowner mows the lawn every Wednesday afternoon. Sketch a rough graph of the height of the grass as a function of time over the course of a four-week period.

Khagan Gulusoy · Accepted Answer

Let’s describe how the height of the grass changes during a week. The grass grows from Sunday till Wednesday afternoon, until the homeowner mows the lawn. After that, the height of the grass starts rising again until Saturday. Since we analyze a four-week period, the graph of the function will approximately look as follows:
\begin{figure}[H] \centering
\begin{tikzpicture}[scale=0.85]
    \begin{axis}[axis lines=left,width=10cm,height=6cm,xmin=0,xmax=17,ymin=0,ymax=6,xtick={2,6,10,14},xticklabel={Wed},ytick=none,xlabel={$t$, time}, ylabel={$h$, height}]
         \addplot[domain=0:2, samples=2, mark=none, color=red, ultra thick] {x+3}; 
         \addplot[domain=2:6, samples=2, mark=none, color=red, ultra thick] {x-1}; 
         \addplot[domain=6:10, samples=2, mark=none, color=red, ultra thick] {x-5}; 
         \addplot[domain=10:14, samples=2, mark=none, color=red, ultra thick] {x-9};
         \addplot[domain=14:16, samples=2, mark=none, color=red, ultra thick] {x-13};
         % t=0
         \addplot[mark=*, mark options={scale=1, fill=red}] coordinates {(0,3)};
         % t=2
         \addplot[mark=*, mark options={scale=1, fill=white}] coordinates {(2,5)};
         \addplot[mark=*, mark options={scale=1, fill=red}] coordinates {(2,1)}; 
         \addplot +[dashed,gray,mark=none] coordinates {(2,5) (2,1)};
         % t=6
         \addplot[mark=*, mark options={scale=1, fill=white}] coordinates {(6,5)};
         \addplot[mark=*, mark options={scale=1, fill=red}] coordinates {(2,1)};
         \addplot +[dashed,gray,mark=none] coordinates {(6,5) (2,1)};
         %t=8
         \addplot[mark=*, mark options={scale=1, fill=white}] coordinates {(6,5)};
         \addplot[mark=*, mark options={scale=1, fill=red}] coordinates {(6,1)};
         \addplot +[dashed,gray,mark=none] coordinates {(6,5) (6,1)};
         % t=10
         \addplot[mark=*,mark options={scale=1, fill=white}] coordinates {(10,5)};
         \addplot[mark=*, mark options={scale=1, fill=red}] coordinates {(10,1)};
         \addplot +[dashed,gray,mark=none] coordinates {(10,5) (10,1)};
         % t=14
         \addplot[mark=*, mark options={scale=1, fill=white}] coordinates {(14,5)};
         \addplot[mark=*, mark options={scale=1, fill=red}] coordinates {(14,1)};
         \addplot +[dashed,gray,mark=none] coordinates {(14,5) (14,1)};
         \addplot[mark=*, mark options={scale=1, fill=red}] coordinates {(16,3)};
    \end{axis}
\end{tikzpicture}
\end{figure}

Exercise 1.1.29

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Exercise 1.1.29

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