How to create a parabolic formula - For Weight Loss

In summary, the conversation is about creating a parabolic or logarithmic formula to track weight loss, with the goal of reaching a target weight in 112 days. There are concerns about the aggressiveness of the weight loss plan and suggestions to use a linear or exponential function instead. It is also mentioned that the given information is not enough to determine a specific function and more details are needed.
  • #1
tomtomtom1
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TL;DR Summary
How to create a parabolic formula
Hello all

I was hoping someone can help with the following problem.

I am trying to create a parabolic formula to give me target weight.

For example:-

Day 1 = Target Weight 100kg
Day 112 = Target Weight 67kg

Each day is consecutive - can anyone help me to create a parabolic formula that goes from 100kg in Day 1 down to 67kg in Day 112.

A linear equation is easier but doesn't do it for me a parabolic formula would

Can anyone help?

Thank you.
 
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  • #2
Do you maybe mean exponential instead of parabolic? It makes a difference what you want to base the non-linear term in your equation on (just time or the previous day's weight)...
 
  • #3
A couple of cautionary words - in case this is an actual weight loss plan:

1. That's an extremely aggressive timetable. 72 lb. in 112 days - or two pounds every three days. One might call it dangerous. Medical opinions vary, but a good ballpark figure for weight loss is more like 1-2 pounds (.5kg-1kg) per week.

2. If you follow through, you have a date with a hospital for dehydration and electrolyte imbalance (which leads to a heart attack).

3. There is no point in weighing yourself more often than once per week. Your normal weight will vary by several pounds per day - trying to track it any more frequently than weekly will give false readings of your true weight loss.
 
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  • #4
tomtomtom1 said:
Summary:: How to create a parabolic formula

I was hoping someone can help with the following problem.

I am trying to create a parabolic formula to give me target weight.
@tomtomtom1 (if that is your REAL name...) -- Is this more homework?
 
  • #5
From the mathematical side, a parabola has three degrees of freedom, you only fixed two. There is e.g. a parabola that has the given start and end numbers but goes through 1000 kg in between. There is also a parabola that goes through -100 kg in between. Clearly these examples are nonsense, but there is still a large range of non-nonsense parabolas and no rule given to distinguish between them.

I also don't see what a parabola would do better than a linear function. Keeping the same weight loss per week is easier and probably better for the body, too. And keep the advice of post 3 in mind.
 
  • #6
mfb said:
From the mathematical side, a parabola has three degrees of freedom, you only fixed two. There is e.g. a parabola that has the given start and end numbers but goes through 1000 kg in between. There is also a parabola that goes through -100 kg in between. Clearly these examples are nonsense, but there is still a large range of non-nonsense parabolas and no rule given to distinguish between them.

I also don't see what a parabola would do better than a linear function. Keeping the same weight loss per week is easier and probably better for the body, too. And keep the advice of post 3 in mind.

Hi mfb

Would some form of logarithmic function work?
 
  • #8
berkeman said:
Do you maybe mean exponential instead of parabolic? It makes a difference what you want to base the non-linear term in your equation on (just time or the previous day's weight)...
Berkeman

If an exponential/log function would meet Day 1 = 100kg and Day 112 = 67kg then i would be happy to try that but i just don't know how to generate the function that meets those requirements.
 
  • #9
berkeman said:
@tomtomtom1 (if that is your REAL name...) -- Is this more homework?
You didn't respond to @berkeman's question.

An exponential function (decaying) would look like this: ##W(x) = W_0e^{-kx}##, where k is a positive constant. Using your given information, W(1) = 100 and W(112) = 67, I get an exponential function that is close to being a straight line.
 
  • #10
tomtomtom1 said:
If an exponential/log function would meet Day 1 = 100kg and Day 112 = 67kg then i would be happy to try that but i just don't know how to generate the function that meets those requirements.
Pick any function whatsoever. If it does not happen to hit the points where W(1)=100 and W(112)=67 then add a linear function to make up the difference.

This would be a [trivial] example of Lagrange interpolation.

A different approach is the one that @Mark44 used. Find a function that has two or more tunable parameters and tune them so that W(1) = 100 and W(112) = 67.
 
  • #11
I think jedish's question really needs an answer: is this homework?

Because if it isn't, one must ask how much use it can be. If the OP is
- measuring OP's weight daily,
- and that can vary by as much as a kg,
- and OP's scale only measures to a precision of one kg
- and OP is trying to track a curve that varies by less than one kg per day...
weight loss.png

Also notice that - to hit the target weight by the target date and maintain a slope that levels off the farther one goes - the initial slope must be steeper than average i.e. the OP will have to lose a greater than average weight in the first few weeks.

Essentially the OP has to lose something on the order of 1 kg every two days for the first couple of weeks.

Good luck doing that without suffering dehydration - or worse.
 
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Related to How to create a parabolic formula - For Weight Loss

1. What is a parabolic formula for weight loss?

A parabolic formula for weight loss is a mathematical equation that describes the relationship between weight loss and time. It is based on the concept of parabolas, which are curved shapes that can be used to model various phenomena.

2. How do I create a parabolic formula for weight loss?

To create a parabolic formula for weight loss, you will need to collect data on weight loss over time. This data can then be plotted on a graph, with weight on the vertical axis and time on the horizontal axis. The curve that best fits the data points will be the parabolic formula for weight loss.

3. What factors should be included in a parabolic formula for weight loss?

A parabolic formula for weight loss should take into account factors such as initial weight, target weight, and the rate of weight loss. It may also include variables such as age, gender, and activity level.

4. Can a parabolic formula for weight loss be used for everyone?

No, a parabolic formula for weight loss may not be suitable for everyone. It is important to consult with a healthcare professional before using any weight loss formula, as individual factors and health conditions may affect the effectiveness of the formula.

5. Are there any limitations to using a parabolic formula for weight loss?

While a parabolic formula for weight loss can be a helpful tool, it should not be the only method used for weight loss. Other factors such as diet, exercise, and overall lifestyle should also be considered. Additionally, the formula may need to be adjusted over time as weight loss progresses.

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