Function Describing Caloric Target

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In summary, the conversation discusses a function that describes the change in weight over time based on various constant variables. The function is modified to allow for variable values of a constant daily caloric target. The individual is seeking help in solving for the unknown value of the constant caloric target given the other known constant values and equations. The conversation also mentions a linear relationship between weight and baseline caloric expenditure.
  • #1
CaseyJRichard
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[Heavily edited for clarity.]

So, I'm playing around with a function that describes the change of an individuals weight as a function of days passed given a number of constant variables: current weight, target weight, number of days until target weight will be reached, and daily calorie target.

My function is derived from an equation that describes weight after a number of days given a constant caloric deficit, d:

f(0) = a;
f(x+1) = f(x) - (d/3500)
f(n) = b;

With this set of equations, we can solve for d (daily caloric deficit) given a (starting weight), b (ending weight), and n (number of days until ending weight is reached).

That's fine, but I wanted to alter this set of equations to allow for variable values of d. So, I removed d as a constant variable and allowed it to equal g(x)-t where g(x) is a calculated caloric baseline. Now I want to solve for a constant value t (a constant daily caloric target) that would result in a decrease to weight b after n days given a starting weight a.

f(0) = a; // where a is current weight
g(x) = q + p*f(x); // this describes a linear relationship between caloric baseline and weight
f(x+1) = (g(x)-t)/3500; // t is the constant caloric target, so g(x)-t is caloric deficit.
f(n) = b; // n = number of days until target weight will be reached. b = target weight.

Of course, f(x+1) and g(x) could be combined; I kept the separate to illustrate the model.

Now, my question is... how would I solve for t if a, n, b, q, and p are all known? I intuitively known there is a way to solve this, but I can't figure it out, and it's bugging me. If anyone could help me figure this out, I'd appreciate it.

Edit: by the way, if this isn't calculus... my bad.
 
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  • #2
Not exactly "Calculus" but close to it. This is, technically, a "finite difference equation" but a simple one. If f(0)= a then f(1)= f(0+ 1)= a- d/3500, f(2)= f(1+ 1)= (a- d/3500)- d/3500= a- 2d/3500, f(3)= f(2+ 1)= (a- 2d/3500)- d/3500= a- 3d/3500, and, in general f(x)= a- 3x/3500.

g(x) = q + p*f(x); // q and p define the line that approximate a given individuals caloric baseline as a function of weight.
So g(x)= q+ pa- 3px/3500. But I don't understand what you mean by "line that approximates a given individuals caloric baseline as a function of weight".

f(x+1) = (g(x)-t)/3500; // t is the constant caloric target, so g(x)-t is caloric deficit.
You have already said that f(x+1)= f(x)- d/3500 and that g(x)= q+ pf(x). So f(x+1)= (g(x)- t)/3500 is f(x)- d/3500= (q+ pf(x)- t)/3500= (q- t)/3500+ pf(x)/3500. Then f(x)- pf(x)/3500= (1- p/3500)f(x)= (d+ q- t)/3500 and f(x)= [(d+ q- t)/3500][3500/(3500- p)]
f(x)= (d+ q- t)/(3500- p) which can't be correct because there is no "x" on the right side. Given that d, q, t, and p are constant, the right side stays the same no matter how x changes.
 
  • #3
Oh, I see. No, I guess I was confusing. The first function is actually describing a different model than the latter four, and for the sake of "solving the problem" doesn't exist. (It's describing a model with constant caloric deficit and a steadily decreasing daily target caloric intake, whereas the other four are describing steadily decreasing caloric deficit and constant daily caloric intake. I just provided the former equation as background info, to show where I was coming from before I found this problem.

I'm just trying to find the equation that solves for the unknown value of t with respect to the other (known) constant values (d, q, t, p, and n) given only the latter four equations.

If that makes sense. :\

(I heavily edited my original post to clarify this.)

EDIT: I just meant there is an approximately linear relationship between weight ("f(x)") and baseline caloric expenditure ("g(x)") when other factors (age, height, gender, etc...) are held constant. Incidentally, "g(x) = q + p*f(x)" is that line.
 
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Related to Function Describing Caloric Target

What is a "Function Describing Caloric Target"?

A Function Describing Caloric Target is a mathematical equation that calculates the amount of calories an individual should consume in a day based on factors such as age, gender, weight, and activity level.

How is a Function Describing Caloric Target calculated?

A Function Describing Caloric Target is typically calculated using the Harris-Benedict equation, which takes into account an individual's basal metabolic rate (BMR) and activity level. The BMR is the amount of energy needed to maintain basic bodily functions at rest, while the activity level takes into account physical activity.

Why is it important to know your Function Describing Caloric Target?

Knowing your Function Describing Caloric Target can help you maintain a healthy weight and meet your nutritional needs. Consuming too many or too few calories can lead to weight gain or loss, and can also impact overall health and well-being.

How accurate is a Function Describing Caloric Target?

While a Function Describing Caloric Target can provide a general guideline for caloric intake, it is not a perfect measure. Factors such as genetics, hormones, and individual metabolism can also impact caloric needs. Additionally, the equation may not account for certain medical conditions or dietary restrictions. It is best to consult with a healthcare professional for personalized recommendations.

Can a Function Describing Caloric Target be used for weight loss?

Yes, a Function Describing Caloric Target can be used as a starting point for weight loss. By calculating the number of calories needed to maintain weight, you can create a calorie deficit to promote weight loss. However, it is important to also consider the quality of the calories consumed and to engage in regular physical activity for optimal health.

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