title: Distribution of decreasing quantity over X number of days
body: <p>I am trying to graph the delivery distribution of a known quantity in a decreasing fashion over X number of days.  I need help with a formula which I can implement in php.</p>
  
  <p>The constants would be 10,000 units, and a start value of 300% of an averaged distribution (sorry for the poor terms).</p>
  
  <p>For example:</p>
  
  <p>10,000 units will be distributed over 10 days.  The first day would had have a delivery of 300% higher than a regular average, so 3,000.  The number will fall over the next 9 days until all have been delivered.</p>
  
  <p>I can fudge the above example via excel by figuring out a coefficient to multiple each delivery by to reduce it (this example is .71).  </p>
  
  <p><a href="https://imgur.com/68KSyGs" rel="nofollow noreferrer"><img src="https://i.imgur.com/68KSyGs.png" title="Hosted by imgur.com" /></a></p>
  
  <p>I will be implementing this in php.  The days can range from anywhere from as small as 3 days to 365 days.  </p>
  
  <p>So ideally the solution would allow me to do something along the following:</p>
  
  <pre><code>$units = array();
  $startValue = (10000 / $daysToDeliver) * 3;
  for ($x= 0, $x &lt; $daysToDeliver, $x++) {
     //add the next deliver quantity onto the array
     $units[] = awesomefunction($lastDeliverAmount, $daysLeftToDeliver);  // guessing here
  }
  </code></pre>
  
  <p>I know I'm over simplifying the inputs on the function, just trying to give a rough idea.</p>
  
  <p>Thank you for your time and consideration!</p>