Handwriting font lowcase letters and math

Question

How can I make the math formular also as handwritten? And can I make the letters in the handwritten be as written on screen with lower case?

As you can see both g af b are written as G and B.

    \documentclass[border=1 cm]{standalone}
\usepackage{pgfplots,tikz}

\pgfplotsset{compat=1.18}
\usepackage[T1]{fontenc}
\DeclareRobustCommand{\augiefamily}{%
    \fontfamily{augie}\fontseries{m}\fontshape{n}\selectfont}
\DeclareTextFontCommand{\textaugie}{\augiefamily}



\begin{document}
    
        \begin{tikzpicture}
    \node at (0,0) {$f(x)=b\cdot a^x$};
    \node[scale=0.4, blue] at (2.5,-0.2) {\augiefamily Eksponenten, den uafhængige variabel};
    \node[scale=0.4, orange] at (1.6,-0.6) {\augiefamily Fremskrivningsfaktoren};
    \node[scale=0.4, red] at (1.2,0.5) {\augiefamily Skæring med y-aksen};
    
    \draw[->,red] (0.4,0.5) to[out=180,in=90] (0.27,0.25);
    \draw[->,blue] (1.1,-0.2) to[out=180,in=270] (0.88,0);
    \draw[->,orange] (1,-0.5) to[out=140,in=270] (0.7,-0.15);
            
    \end{tikzpicture}   
\end{document}

Answer 1

If you are able to switch to xelatex or lualatex and have augie installed as font on your computer, you could do something like this:

% !TeX TS-program = lualatex

    \documentclass[border=1cm,beamer,crop]{standalone}
\usepackage{pgfplots,tikz}

\pgfplotsset{compat=1.18}
\usepackage{fontspec}
\setsansfont{augie}



\begin{document}
    
        \begin{tikzpicture}
    \node at (0,0) {$f(x)=b\cdot a^x$};
    \node[scale=0.4, blue] at (2.5,-0.2) { Eksponenten, den uafhængige variabel};
    \node[scale=0.4, orange] at (1.6,-0.6) { Fremskrivningsfaktoren};
    \node[scale=0.4, red] at (1.2,0.5) { Skæring med y-aksen};
    
    \draw[->,red] (0.4,0.5) to[out=180,in=90] (0.27,0.25);
    \draw[->,blue] (1.1,-0.2) to[out=180,in=270] (0.88,0);
    \draw[->,orange] (1,-0.5) to[out=140,in=270] (0.7,-0.15);
            
    \end{tikzpicture}   
\end{document}