Question 256080
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Well, that depends.  Do you mean that the patient is supposed to lose 3% of 200kg (i.e. 6kg) each week, or is he supposed to lose 3% of the current weight each week?


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{200\ -\ 80}{6}\ =\ 20] weeks.


Or


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 200\left(1.00\,-\,0.03\right)^w\ =\ 80]



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \ln\{200\left(1.00\,-\,0.03\right)^w\}\ =\ \ln(80)]



*[tex \LARGE \ \ \ \ \ \ \ \ \ \ w\ = \frac{\ln\left(\frac{80}{200}\right)}{\ln(0.97)}\ \approx\ 30] weeks


Except that neither answer is correct in practical terms.  In order to lose 1kg per week, a person needs to have a caloric deficit of about 1100 calories PER DAY.  So 6 kg per week means a 6600 calorie PER DAY deficit, i.e. a combination of eating less and exercising more.  Even at 440 lbs, at a 6600 calorie per day deficit, the poor schmuck would probably die from malnourishment and dehydration within 2 or three weeks.  0.5% per week, at least at the outset, is more like what would be a safe rate of weight loss. 


John
*[tex \LARGE e^{i\pi} + 1 = 0]
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