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Question # A store sells custom circular rugs. The table shoes the costs c(in dollars) of rugs that have diameter's of d feet. Let the diameter d represent the independent variable. Tell whether the data can be modeled by a linear, an exponential, or quadratic function.

Modeling data distributions
ANSWERED A store sells custom circular rugs. The table shoes the costs c(in dollars) of rugs that have diameter's of d feet. Let the diameter d represent the independent variable. Tell whether the data can be modeled by a linear, an exponential, or quadratic function. 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.