Construct a Scatterplot and Identify the Mathematical Model That Best $\mathrm { R } ^ { 2 }$

question 107

Multiple Choice

Construct a scatterplot and identify the mathematical model that best fits the data. Assume that the model is to be used
only for the scope of the given data and consider only linear, quadratic, logarithmic, exponential, and power models. Use
a calculator or computer to obtain the regression equation of the model that best fits the data. You may need to fit several
models and compare the values of $\mathrm { R } ^ { 2 }$
-A rock is dropped from a tall building and its distance (in feet) below the point of release is recorded as accurately as possible at various times after the moment of release. The results are shown in the table. Find the
Regression equation of the best model. $\begin{array}{l|llllll}\mathrm{x} \text { (seconds after release) } & 1 & 2 & 3 & 4 & 5 & 6 \\\hline \mathrm{y} \text { (distance in feet) } & 16 & 63 & 146 & 255 & 403 & 572\end{array}$

• A) \(y = 13.0 \mathrm { e } ^ { 0.686 \mathrm { x } }\)
• B) \(y = - 74.9 + 290 \ln x\)
• C) \(y = - 148.4 + 112 x\)
• D) \(\mathrm { y } = 15.95 \mathrm { x } ^ { 2 }\)

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Definitions:

Utility Function

A mathematical representation of how a consumer's preferences over a set of goods and services translates into an assessment of the utility or satisfaction derived from each bundle of consumption.

Indifference Curve

A graph representing different combinations of two goods that provide a consumer with the same level of satisfaction or utility.

Apples

Edible fruits produced by an apple tree, characterized by a sweet flavor and crisp texture, often consumed raw or used in a variety of culinary dishes.

Bananas

A long curved fruit that grows in clusters and has soft pulpy flesh and yellow skin when ripe.