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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 ford(daily caloric deficit) givena(starting weight),b(ending weight), andn(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 ofd. So, I removeddas a constant variable and allowed it to equalg(x)-twhereg(x)is a calculated caloric baseline. Now I want to solve for a constant valuet(a constant daily caloric target) that would result in a decrease to weightbafterndays given a starting weighta.

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, sog(x)-tis 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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# Function Describing Caloric Target

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