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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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