Construct a Scatterplot and Identify the Mathematical Model That Best

question 15

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 R²
-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) \(y = - 74.9 + 290 \ln x\)
• B) \(y = - 148.4 + 112 x\)
• C) \(y = 13.0 \mathrm { e } ^ { 0.686 x }\)
• D) \(y = 15.95 x ^ { 2 }\)

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Definitions:

Series Connection

An electrical circuit configuration in which components are linked in a sequential manner, so the same current flows through each component without branching.

Frequency Source

An electronic component or circuit that generates a specific frequency or range of frequencies, often used in telecommunications and signal processing.

Capacitive Reactance

The measure of a capacitor's opposition to changes in voltage, affecting AC flow without dissipating energy, inversely proportional to the frequency.

Series Connection

A type of circuit configuration where components are connected end-to-end, and the current flows through one component to get to the next.