Keys in your $options array are not actual ID's of database rows.
So your $options array looks like this:
Array(
'0' => array('id'=>'10', 'value'=>'someval1'),
'1' => array('id'=>'22', 'value'=>'someval2'),
'2' => array('id'=>'36', 'value'=>'someval3'))
To see this, put print_r($options);
before echo call.
To make real dropdown you should make helper function that looks like this:
function my_form_dropdown($name, $result_array){
$options = array();
foreach ($result_array as $key => $value){
$options[$value['id']] = $value['value'];
}
return form_dropdown($name, $options);
}