ExcelWriter format number to currency by column name

I'm converting the float columns to currency data type with the following:

df = pd.DataFrame({'col0': [71513.0, 200000.0, None], 
                    'col1': [True, False, False], 
                    'col2': [100.0, 200.0, 0.0]})
df[['col0', 'col2']] = df[['col0', 'col2']].astype(float).astype("Int32").applymap(\
                            lambda x: "${:,.0f}".format(x) if isinstance(x, int) else x)

I am outputting the table with the following:

writer = pd.ExcelWriter('output.xlsx', engine='xlsxwriter')
df.to_excel(writer, index= False)
workbook  = writer.book
ws = writer.sheets['Sheet1']
writer.close()
writer.save()

However, when I output the datable with the following, the currency is stored as text:

How would I format the excel sheet itself (instead of the pandas column) based on the column name so that the value is a number, but the formatting is currency?

This is how it worked for me

Removed the column formatting within df

df = pd.DataFrame({'col0': [71513.0, 200000.0, None], 
                    'col1': [True, False, False], 
                    'col2': [100.0, 200.0, 0.0]})

Removed index parameter from to_excel, Defined format for the columns, and assign it to columns 1, and 3

writer = pd.ExcelWriter('output.xlsx', engine='xlsxwriter')
df.to_excel(writer)  # index= False)

workbook  = writer.book
ws = writer.sheets['Sheet1']

format1 = workbook.add_format({'num_format': '$#,##0.00'})

ws.set_column(1, 1, 18, format1)
ws.set_column(3, 3, 18, format1)
writer.save()
writer.close()

reference to documentation: https://xlsxwriter.readthedocs.io/example_pandas_column_formats.html