I recently asked a question to find a formula for a fiction project. I was met with a brilliant answer; but, I am missing key pieces of information to arrive at how the answer is wholly implemented.
Fiction Author Searching For Formula.
I would like to know how the constant representing the mouse (0.259) or wolf (5.021) was reached-so I would be able to alter a constant (likely the wolf) using a different animal, as to change the degree of scaling.
As an example, if we used a 4ft mouse and 12ft elephant as constants; how do I arrive at the 0.259 (mouse) and whatever number the elephant would be? What was the mathematical process?
This way I would be able to convert any two animals into constants and have more control of the scale.
If I understand correctly, you want to determine heights using the formula $$ \text{height} = a + b \log(\text{weight}). $$ Plugging in the height and weight of the mouse, we find that $$ \tag{$\heartsuit$} 4 = a + b \log(.019). $$ Plugging in the height and weight of the elephant, we find that $$ \tag{$\spadesuit$}12 = a + b \log(7000). $$ Now let's use equation ($\heartsuit$) to solve for $a$. Subtracting $b \log(.019)$ from both sides of the equation, we find that $$ \tag{$\clubsuit$}a = 4 - b \log(.019). $$ Next, let's plug this value for $a$ into equation ($\spadesuit$). This gives us $$ 12 = 4 - b \log(.019) + b \log(7000). $$ Solving for $b$, we find that $$ b = \frac{-8}{\log(.019) - \log(7000)} \approx .62417. $$ Finally, plug this value for $b$ into equation ($\clubsuit$) to get $a$.