Upgraded to PHP 7.0 and now get a PHP Fatal Error: "Call to undefined function mysql_connect()&

I've been trying to figure out how to fix this issue. I know that PHP 7.0 deprecated the mysql_connect function in favor of mysqli_connect... but what do I need to do to fix this? It seems to be an issue with /wp-includes/wp-db.php:1520. So this means that I'd have to edit a core file? Doesn't the mean that it'll get replaced next time I upgrade WordPress?

I'm running Ubuntu 14.04 on a VPS if that helps. Using Wordpress Multisite (latest version).

Here's the last few lines of my /var/log/apache2/error.log

[Thu Apr 07 07:59:00.835950 2016] [:error] [pid 635] [client 66.249.65.148:59579] PHP Fatal error:  Uncaught Error: Call to undefined function m
ysql_connect() in /var/www/html/wp-includes/wp-db.php:1520\nStack trace:\n#0 /var/www/html/wp-includes/wp-db.php(658): wpdb->db_connect()\n#1 /v
ar/www/html/wp-includes/load.php(368): wpdb->__construct('wordpress', '[REMOVED]', 'wordpress', 'localhost')\n#2 /var/www/html/wp-settings.php(
88): require_wp_db()\n#3 /var/www/html/wp-config.php(114): require_once('/var/www/html/w...')\n#4 /var/www/html/wp-load.php(37): require_once('/
var/www/html/w...')\n#5 /var/www/html/wp-blog-header.php(12): require_once('/var/www/html/w...')\n#6 /var/www/html/index.php(17): require('/var/
www/html/w...')\n#7 {main}\n  thrown in /var/www/html/wp-includes/wp-db.php on line 1520
[Thu Apr 07 07:59:08.456531 2016] [:error] [pid 32285] [client 192.0.102.40:46303] PHP Fatal error:  Uncaught Error: Call to undefined function
mysql_connect() in /var/www/html/wp-includes/wp-db.php:1520\nStack trace:\n#0 /var/www/html/wp-includes/wp-db.php(658): wpdb->db_connect()\n#1 /
var/www/html/wp-includes/load.php(368): wpdb->__construct('wordpress', '[REMOVED]', 'wordpress', 'localhost')\n#2 /var/www/html/wp-settings.php
(88): require_wp_db()\n#3 /var/www/html/wp-config.php(114): require_once('/var/www/html/w...')\n#4 /var/www/html/wp-load.php(37): require_once('
/var/www/html/w...')\n#5 /var/www/html/wp-blog-header.php(12): require_once('/var/www/html/w...')\n#6 /var/www/html/index.php(17): require('/var
/www/html/w...')\n#7 {main}\n  thrown in /var/www/html/wp-includes/wp-db.php on line 1520
[Thu Apr 07 07:59:32.814471 2016] [:error] [pid 649] [client 66.249.79.91:56286] PHP Fatal error:  Uncaught Error: Call to undefined function my
sql_connect() in /var/www/html/wp-includes/wp-db.php:1520\nStack trace:\n#0 /var/www/html/wp-includes/wp-db.php(658): wpdb->db_connect()\n#1 /va
r/www/html/wp-includes/load.php(368): wpdb->__construct('wordpress', '[REMOVED]', 'wordpress', 'localhost')\n#2 /var/www/html/wp-settings.php(8
8): require_wp_db()\n#3 /var/www/html/wp-config.php(114): require_once('/var/www/html/w...')\n#4 /var/www/html/wp-load.php(37): require_once('/v
ar/www/html/w...')\n#5 /var/www/html/wp-blog-header.php(12): require_once('/var/www/html/w...')\n#6 /var/www/html/index.php(17): require('/var/w
ww/html/w...')\n#7 {main}\n  thrown in /var/www/html/wp-includes/wp-db.php on line 1520, referer: https://arkonlabs.com/store/
[Thu Apr 07 08:00:39.426229 2016] [:error] [pid 636] [client 192.0.101.226:33314] PHP Fatal error:  Uncaught Error: Call to undefined function m
ysql_connect() in /var/www/html/wp-includes/wp-db.php:1520\nStack trace:\n#0 /var/www/html/wp-includes/wp-db.php(658): wpdb->db_connect()\n#1 /v
ar/www/html/wp-includes/load.php(368): wpdb->__construct('wordpress', '[REMOVED]', 'wordpress', 'localhost')\n#2 /var/www/html/wp-settings.php(
88): require_wp_db()\n#3 /var/www/html/wp-config.php(114): require_once('/var/www/html/w...')\n#4 /var/www/html/wp-load.php(37): require_once('/
var/www/html/w...')\n#5 /var/www/html/wp-blog-header.php(12): require_once('/var/www/html/w...')\n#6 /var/www/html/index.php(17): require('/var/
www/html/w...')\n#7 {main}\n  thrown in /var/www/html/wp-includes/wp-db.php on line 1520
[Thu Apr 07 08:01:09.678262 2016] [:error] [pid 643] [client 107.140.25.242:59394] PHP Fatal error:  Uncaught Error: Call to undefined function
mysql_connect() in /var/www/html/wp-includes/wp-db.php:1520\nStack trace:\n#0 /var/www/html/wp-includes/wp-db.php(658): wpdb->db_connect()\n#1 /
var/www/html/wp-includes/load.php(368): wpdb->__construct('wordpress', '[REMOVED]', 'wordpress', 'localhost')\n#2 /var/www/html/wp-settings.php
(88): require_wp_db()\n#3 /var/www/html/wp-config.php(114): require_once('/var/www/html/w...')\n#4 /var/www/html/wp-load.php(37): require_once('
/var/www/html/w...')\n#5 /var/www/html/wp-blog-header.php(12): require_once('/var/www/html/w...')\n#6 /var/www/html/index.php(17): require('/var
/www/html/w...')\n#7 {main}\n  thrown in /var/www/html/wp-includes/wp-db.php on line 1520