创作半衰期情节

Question

我正在尝试在 LaTeX 中复制下面的图，但我对编码有点迷茫。不需要数学。这只是一个练习，创建类似于指数衰减的通用图。我想复制 y 轴标签，其中 y_0、\frac{y_0}{2} 和 x 轴上的 \tau。

我的尝试

\documentclass{amsart}
\usepackage{pgfplots}
\pgfplotsset{compat=1.8}
\usepackage{mathtools}
\usepackage{tikz}
\begin{document} 

\begin{tikzpicture}
 \begin{axis}[
   scaled ticks=false,
   xmin=0,
   ymin=0,
   xlabel=x,
   ylabel=y ,
   ]
    \addplot[domain=0:5, black, ultra thick,smooth] {e^(-x)};
    \addplot[domain=0:0.7, gray, dashed] {0.5};   
\end{axis}
\end{tikzpicture}

Answer 1

这里有一个例子，尽可能地模仿您的图中的风格。

\documentclass{amsart}
\usepackage{pgfplots}
\pgfplotsset{compat=1.8}
\usepackage{mathtools}
%\usepackage{tikz} %load by pgfplots
\begin{document} 
\begin{tikzpicture}
 \begin{axis}[
   xmin=0,
   xmax=2.1,
   ymin=0,
   ymax=1.3,
   tick style={draw=none},
   xtick={-ln(0.5)},
   ytick={0.5,1},
   xticklabels={$\tau$},
   xticklabel style={font=\Large},
   yticklabels={$\displaystyle\frac{y_0}{2}$,$y_0$},
   yticklabel style={font=\Large},
   xlabel=$t$,   
   ylabel=$y$,
   axis lines=center,
   axis line style ={thick,-latex},
   x label style={anchor=west},
   y label style={anchor=south}
   ]
    \addplot[domain=0:2, black, ultra thick,smooth] {e^(-x)};
    \draw [thick,dotted] (axis cs:0,0.5) -- (axis cs:{-ln(0.5)},0.5) -- (axis cs:{-ln(0.5)},0);
\end{axis}
\end{tikzpicture}
\end{document}

Answer 2

有了图书馆intersection

\documentclass{amsart}
\usepackage{pgfplots}
\pgfplotsset{compat=1.18}
\usetikzlibrary{intersections}
\usepackage{mathtools}
% \usepackage{tikz}%<-- loaded by pgfplots
\begin{document} 

\begin{tikzpicture}
  \begin{axis}[
    clip=false,
    declare function={
      f(\x)=e^(-\x);
      },
    scaled ticks=false,
    axis lines=center,
    xmin=0,
    ymin=0,
    xmax=5.2,
    ymax=1.2,
    xlabel=t,
    ylabel=y,
    xlabel style={
      at={(1,0)},
      anchor=west,
      },
    ylabel style={
        at={(0,1)},
        align=right,
        anchor=south,
        },
    tick style={draw=none},
    xtick=\empty,ytick=\empty,
    ]
    \addplot[name path=curve,domain=0:5, black, ultra thick,smooth] {f(x)};
    \path [name path=line] (axis cs:0,0.5) -- (axis cs:5,0.5);
    %
    \fill [red, opacity=0.5, name intersections={of=line and curve}]
    (intersection-1) circle (2pt);
    \draw[name intersections={of=line and curve}] [dashed](intersection-1)-|(axis cs:0,0)node[pos=0.5,xshift=-2ex,red]{$\dfrac{y_0}{2}$};
    \draw[name intersections={of=line and curve}] [dashed](intersection-1)|-(axis cs:0,0)node[pos=0.5,yshift=-1ex,red]{$\tau$};
  %
    \node[xshift=-2ex,red]at(axis cs:0,1){$y_0$};
  \end{axis}
\end{tikzpicture}
\end{document}

Answer 3

像这样：

代码 （tikz）：

\documentclass[margin=20pt]{standalone}
\usepackage{tikz}
%\usetikzlibrary{calc}

\begin{document}    
    \begin{tikzpicture}
        \draw[gray!30] (0,0) grid (6,6);
        \draw[cyan,line width=2pt] plot[domain=0:6,smooth,samples=60] (\x,{6*2^(-\x)});
        \draw[-latex] (0,0)--(6,0);
        \draw[-latex] (0,0)--(0,6.5);
        \foreach \x in {0,1,...,6} 
            \draw (\x,0)--(\x,-3pt) node[below] () {\small \x$\tau$};
        \draw (0,6) node[left] () {$y_0$};
        \draw (0,3) node[left] () {$\frac{y_0}{2}$};
    \end{tikzpicture}   
\end{document}

Answer 4

和tzplot：

\documentclass{standalone}

\usepackage{tzplot}

\begin{document}

\begin{tikzpicture}[yscale=2]
\tzaxes(3,1.3){$t$}{$y$}
\def\Fx{exp(-\x)}
\tzfn\Fx[2.5:0]{$y_0$}[l]
\tzvXpointat{Fx}{.8}(X)
\tzproj[densely dotted](X){$\tau$}{$\frac{y_0}{2}$}
\end{tikzpicture}

\end{document}