Mathematica Bar legend for a different function in mathematica

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To add a bar legend for the function g[t] in the provided Mathematica code, the PlotLegends option needs to be integrated correctly within the ParametricPlot. The ColorFunction is already set to use the SolarColors palette, which is rescaled based on the values of g[t]. To implement the bar legend, ensure that the BarLegend is correctly associated with the ColorFunction. The modified code should include the BarLegend directly in the ParametricPlot definition, ensuring it references the same color scaling used in the ColorFunction. This will effectively create a visual representation of the color mapping corresponding to the values of g[t].
djymndl07
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How Can I add bar Legend for g[t] in the following code in mathematica?
Thanks in advance?

f[t_] := t + 1
g[t_] := t^3 + 3*t + 12
ParametricPlot[{f[t]*Cos[\[Theta]], f[t]*Sin[\[Theta]]}, {t, 0, 1}, {\[Theta], 0, 2*Pi},
ColorFunction -> Function[{x, y, t}, ColorData["SolarColors"][Rescale[g[t], {g[0], g[1]}, {0, 1}]]]]
 
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Add
Code: 
PlotLegends -> BarLegend[{"SolarColors", {0, 1}}]
to the ParametricPlot.
 

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