Sounds familiar, wasn't there a program on about this? I'll google it and check it out.
Their Formula prediction is about the same as what I came up with.
Wx = Wf + K • (24 - t)2 ,
where Wx is the subject’s weight at time t and Wf is the final target body weight after 24 weeks. For each subject, the individual factor, K, is determined by the formula,
K = W0/100 • P/242 ,
where W0 is the subject’s initial weight at the beginning of the starvation phase and P is the total desired target weight loss. This quadratic formula for determining calorie intake is called the Key’s Formula and is still used today in the therapeutic treatment of nutritional disorders.