# Colleen and Martin are modeling the data shown. Colleen thinks the model should be f(x)=5.754^x3+2.912x^2−7.516x0.349.

Colleen and Martin are modeling the data shown. Colleen thinks the model should be $$\displaystyle{f{{\left({x}\right)}}}={5.754}^{{x}}{3}+{2.912}{x}^{{2}}−{7.516}{x}{0.349}$$. Martin thinks it should be $$\displaystyle{f{{\left({x}\right)}}}={3.697}{x}^{{2}}+{11.734}{x}−{2.476}$$. Is either of them correct? Explain your reasoning.
$$f(x) -2-190.5-2 -1511.5 00.4243$$

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Anonym

The data suggests that there are two turning points, therefore, a cubic function is a better representation than a quadratic function. Using the cubic regression function on a graphing calculator, we get $$f(x)=5.754x^3+2.912x^2-7.516x+0.349$$