Populate textarea if checkbox is checked

I'm using this to populate a textarea with value if a checkbox is checked:

$('#checkbox_a').change(function(){
    $("#textarea_b").text("");
    if ($('#checkbox_a').is(':checked')) { 
        $("#textarea_b").text("Yes"); 
    }
});

The problem I'm having is that if a user already inputs something in the textarea, decides to delete his input again and marks the checkbox afterwards it won't get populated anymore.

Can you help me with that?