Hard Math question...?

Question

Let's say you did an experiment and you got certain outputs for certain inputs. But instead of solving for x, or an unknown variable, you need to solve for the "steps" to get the specific numbers. You know nothing about the experiment only the numbers given.

What is the equation/formula for these numbers?

For instance,

If A = 1 then B = 16.071067...

A = 2 then B = 19

A = 3 then B = 21.247448...

A = 4 then B = 23.142135...

Also, how did you figure it out? Is this a certain Mathematics branch? Thanks.

Answer 1

Plot it on a graph and try various regressions for best fit.

It's called mathematical modeling.

The curve looks either like a second order polynomial or logarithmic.

.

y= -0.2586x^2 + 3.6389x + 12.707 R^2=0.9998

y= 5.0376ln(x) + 15.863 R^2=0.99

The second order polynomial is a better fit.

Answer 2

"linear relationship" branch of mathematics.

has the property known as a "regression" equation:

B = 14.0 + 2.35 * A

Answer 3

You can do a plot for B vs A. If it looks like a reasonably good straight line then use the least square method to find the straight line equation. You can get better curve-fitting is you use a quadratic. But straight line is the easiest.

Answer 4

plot in a graph to find out what kind of graph it is

Answer 5

So, are you looking for the mathematical pattern in the numbers, or the experimental procedure?

A little confused by what you're asking I guess.

I take it these numbers don't have to be reproducible exactly as they appear??

Answer 6

The branch is statistics, and the method of finding this is called "correlation and regression"

Check it out!

Involves some basic summations, all you do is find the best fit line - defined as - line of least squared distance.

Answer 7

There can be hundreds of ways which can be used to get the given output from the given inputs. Lets say that B is a polynomial of degree n, expressed in terms of A, then

B = x1*A+ x2*A^2 + x3*A^3 + ...

where X1, X2, X3 ... are constants. You can solve the values of these constants by writing equations in terms of A and B.

This was assuming that our function is simple algebraic function. Similarly we can have many more ways of expressing B in terms of A.  

Answer 8

If you expect the answer to be linear, you would use linear regression analysis. If not, you'd need to find a polynomial, exponential, or other function to approximate the data. There are methods for determining those as well.