Given information: It is given with of values (3, 63.90), (4, 113.60), (5, 177.50) and (6, 255.60).
Formula used:
There are three conditions to be followed,
i) If first difference is constant then it is linear function.
ii) If second difference of y values are constant then it is a quadratic function
iii) If ratios of y values are constant then it is exponential function.
Calculation:
Let's find the difference of y values to find whether it is linear or quadratic.
\(\displaystyle{113.60}\ -\ {63.90}={49.7}\)

\(\displaystyle{177.50}\ -\ {113.60}={63.9}\)

\(\displaystyle{255.60}\ -\ {177.50}={78.1}\) Here, the first difference is not a constant so it is NOT a linear function. Now, let's find the second difference of y values \(\displaystyle{63.9}\ -\ {49.7}={14.2}\)

\(\displaystyle{78.1}\ -\ {63.9}={14.2}\) Here the second difference is constant so, it is a quadratic function.

\(\displaystyle{177.50}\ -\ {113.60}={63.9}\)

\(\displaystyle{255.60}\ -\ {177.50}={78.1}\) Here, the first difference is not a constant so it is NOT a linear function. Now, let's find the second difference of y values \(\displaystyle{63.9}\ -\ {49.7}={14.2}\)

\(\displaystyle{78.1}\ -\ {63.9}={14.2}\) Here the second difference is constant so, it is a quadratic function.