Since the data has equally-spaced inputs, we can check whether the data is linear by checking the first difference sequence.
The first difference sequence is not constant, so this data is not linear. Let's check the second difference sequence. This tells whether the data is quadratic or not.
Since the second difference sequence is constant, this data is quadratic and can be modeled by a function of the form S(C)=aC^2+bC+c. Use any three points (C,S) from the table to write a system of equations.
Let's complete the equation of the function with the calculated values of a, b and c.
S(C)=180C^2
Finally, we can substitute 10 for C to estimate the safe working load of the rope that has a circumference of 10 inches.
