How to write a function from a table.

Question

x=2,3,4,5,6

y=20,37,49,66,89

I am trouble determining what type of function is that and have ruled out linear, exponential, and quadratic.

Is this some sort of linear regression? I believe the answer is 16.7x-14.6, but can't figure.

Also, is this possible to figure without a calculator?

Answer 1

If you are given n points you can always fit to it a polynomial

of order n-1.

If this is what your teacher expects then you can fit to your 5 point

a polynomial of order 4:

f(x) = ax⁴ + bx³ + cx² + dx + e

Then you can write 5 equations with 5 variables a, b, c, d, e

f(2) = 20

f(3) = 37

f(4) = 49

f(5) = 66

f(6) = 89

You can then solve the 5 equations and get those 5 coefficients a, b, c, d, e.

And yes, it is possible to figure it out without a calculator

(that is how people did it 50 years ago).

But I do not know anybody who could do it just in his head,

if that is what you mean, or if that is what your teacher expects.