Why do I sink when I exhale in a pool?

As we wrapped up buoyant forces in class this week, I began thinking about my past experiences in a swimming pool. As a kid, I spent a lot of time in a pool, not swimming, just floating and paddling. One thing I noticed floating around in one of my pool session was how I would float and part of my body will be above water when I had a full breath of air. Further, as I exhaled, I slowly sunk deeper into the water. When forcing myself to exhale as much air as possible, without paddling, I would sink to the bottom of the pool. As a young boy, I found it very fun to just sit at the bottom of a pool without moving (only for a short period of time).

Thinking logically, a dead body sinks but living humans can float on their back without moving. This is because without air in our lungs, we are denser than water which means that the force of gravity acting on an airless human body will be greater than the buoyant force of the water. Therefore, as young me exhaled air, my density increased as my volume decreased because I am exhaling air that is less dense than the surrounding water or my body. 

Putting numbers into this phenomenon, according to: https://physics.stackexchange.com/questions/355998/why-do-humans-drown-in-water

humans, with no air in their lungs have a density of about 1.04g/ml which can be converted to 1040kg/m^3. Since pool water has a density of about 1000kg/m^3, it can easily be seen how an airless body will sink. Using the previous values, lung capacity of 6L in adults, air density of 1.225kg/m^3, and my weight of 65kg; we can analyze and calculate the values corresponding to what would happen as I exhaled all the air in a pool.

Initially, with a full breath of 6L air (0.006m^3), my starting density will be 65.00735kg/0.0685m^3= 950kg/m^3. Therefore, with a full breath of air, 5% of my body will be above water which was found through the proportion of the buoyant force with my force of gravity on my mass. From here, I can exhale air to the point where my density equals water. At this stage, I will be in equilibrium and I will be stationary with my whole body submerged. Further, as I continue to exhale, my density approaches the airless density of 1040kg/m^3 as I would continue to accelerate as I sink down to the bottom of the pool.