Increase a float and then slowly reduce the amount of the increase until there is no longer an increase applied.

Score boost function.php

<?php

/***************************************************
* This function takes in a float and returns a float that has been incrased based on the number of days elapsed since creation
* The purpose is to boost a number that is newer and slowly decrease that boost until it is no longer applied after the active period has ended. 
***************************************************/

// Number of days the boost is active - Bounded by 0 and the 
// beginning of the sauce degradation phase.
define(ACTIVE_PERIOD, (float) 5);

// Function that controls the popularity of young posts
function score_boost($social_score, $days_elapsed){
	settype($social_score, "float");
	settype($days_elapsed, "float");

	// Does not allow the Active Period to overlap sauce's decay period
	if(ACTIVE_PERIOD <= 0 || ACTIVE_PERIOD >= 7)
		throw new Exception('Invalid Activity Length');

	// Does not allow boosting beyond the active period
	if ($days_elapsed > ACTIVE_PERIOD)
		throw new Exception('Boost no longer active.');
	
	$k = $social_score/(ACTIVE_PERIOD*ACTIVE_PERIOD);
	return $k*($days_elapsed - ACTIVE_PERIOD)*($days_elapsed - ACTIVE_PERIOD) + $social_score;
}

// Example:
try {
	echo score_boost(14.1, 1), "\n";
} catch (Exception $e) {
	echo 'Caught exception: ', $e->getMessage(), "\n";
}

?>