Instinct to thrive

Let me introduce you to the unicellular organism code-named as:RiruRiru. A cell of RiruRiru, at the end of each day, fragments into rr daughter cells, where 1r41\le r\le 4. The probability of rr taking a certain numerical value, is directly proportional to that value itself. Al the beginning of day 11, one cell of RiruRiru was present in an isolated habitat, with plenty of resources. Find the average RiruRiru population at the beginning of day 2121.

This is part of my set Powers of the ordinary.
Image Credit: Wikimedia Volvocales
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