Update DIV Element Using Custom Javascript on a Wordpress Page

I have a custom WordPress template page that shows a table and when that table was last updated.

Using jQuery/AJAX, I am attempting to use setInterval() to check every second to see if the update time has changed and auto change the div id element showing the updated time.

I have tried reading tutorials. A lot of them show adding files to the /js/ folder, but my theme does not have that directory.

Looking at the different Wordpress plugins, I was only able to locate ones that showed Javascript across all pages, which isn't what I need.

I currently have a tag (see below) at the bottom of my custom page template. I verified that it loads in the page source.

<script type="application/javascript">
  var update_time_function = window.setInterval(update_time, 1000);
  function(update_time) {
    jQuery.ajax({
      url: 'https://website_url.com/last-update/'
      dataType: 'json'
      success: function(utf) {
        jQuery('#update_time').text(utf[0].date_time);
      }
    })
  };
</script>

The expected results should be the div element with the id 'update_time' should be updating, but it not happening. There are no errors in the network console.

The script file is showing in the page source.