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

Question

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

Quizplus · Accepted Answer

The distance a rock falls due to gravity is proportional to the square of the time elapsed, which suggests a quadratic relationship. The correct model is $y = 15.95x^2$, which fits the physical principle of objects in free fall near the Earth's surface, where distance is proportional to the square of time, assuming no air resistance.

Construct a Scatterplot and Identify the Mathematical Model That Best