We notice that after a sudden change in eating habits that daily weight loss can be dramatic. Dieters are discouraged from paying close attention because the pounds lost per day quickly wanes. Here we consider a twist of the calculation that might justify close attention.
Suppose an overweight person suddenly drops all empty calories and cuts even healthy food to palm-sized proportions. What can we expect to happen?
We hypothesize this to be a case of diminishing returns. Some portion of the weight to lose will be lost every day but that portion gets smaller and smaller. Total weight approaches a final weight asymptotically. But what proportion can we expect and what will be the asymptote?
Let's assume a 200 pound person heading towards 150 pounds eventually. We'll also assume that 5% of the weight to lose is gone every day.
200 Current Weight -150 Asymptotic Weight SUM Weight to Lose -0.05 Daily Rate of Loss PRODUCT Expected Loss Today Current Weight SUM Current Weight
What we immediately notice is that when we repeat this calculation tomorrow the results are not as good. Hover over * to make comparisons.
Current Weight Asymptotic Weight SUM Weight to Lose Daily Rate of Loss PRODUCT Expected Loss Today Current Weight SUM Current Weight
Hint: Double-click the first calculation to change numbers to fit your expectations. Refresh the page to propagate these choices to the remaining calculations. Your numbers will be kept privately in your browser.
Our model has two parameters: Asymptotic Weight and Daily Rate of Loss. These are givens in this calculation but unknowns in practice.
Asymptotic Weight depends on the ultimate balance between calories consumed and calories expended though the dynamics can be much more complex. See Metabolic Equivalent of Task to explore expenditure.
Daily Rate of Loss would seem to be a biological time constant that is not often discussed. Some hints at this number appear in discussions of radical weight-loss surgery. Apparently that is the one situation where a step-change in caloric intake regularly occurs. See Half Life.
We will experiment on ourselves with a sudden change of habit. We will fit our daily observations to the model above. (We're recording to a resolution of 0.2 pounds with a balance-beam scale.)
See Weight Change Calculator for our data fitting algorithm. We estimate both rate and limit from observation. We wonder, could we estimate limit more correctly if we knew rate as a physiological given?