Computing score changes based on half-life

decay.php

<?php

$half_time_24h = pow(0.5, 1/24);
$total = 1000;
$score = 700;
$last_update = time() - (3600*1.5); // One and a half hour ago

$new_total = 1010;
$total_delta = $new_total - $total;
$hour_delta = (time() - $last_update) / 3600;

$score = add_and_decay($score, $half_time_24h, $hour_delta, $total_delta);

function add_and_decay($old_score, $hourly_decay, $hour_delta, $add) {
  return $old_score * pow($hourly_decay, $hour_delta) + $add;
}