Crowdedness again In Exercise we looked at United Nations

Chapter 9, Problem 22E

(choose chapter or problem)

At a meeting of the Inter- national Astronomical Union (IAU) in Prague in 2006, Pluto was determined not to be a planet, but rather the largest member of the Kuiper belt of icy objects. Let’s examine some facts. Here is a table of the 9 sun-orbiting objects formerly known as planets:

\(\begin{array}{|l|c|c|c|} \hline \text { Planet } & \begin{array}{c} \text { Position } \\ \text { Number } \end{array} & \begin{array}{c} \text { Distance from Sun } \\ \text { (million miles) } \end{array} & \begin{array}{c} \text { Length of Year } \\ \text { (Earth years) } \end{array} \\ \hline \text { Mercury } & 1 & 36 & 0.24 \\ \text { Venus } & 2 & 67 & 0.61 \\ \text { Earth } & 3 & 93 & 1.00 \\ \text { Mars } & 4 & 142 & 1.88 \\ \text { Jupiter } & 5 & 484 & 11.86 \\ \text { Saturn } & 6 & 887 & 29.46 \\ \text { Uranus } & 7 & 1784 & 84.07 \\ \text { Neptune } & 8 & 2796 & 164.82 \\ \text { Pluto } & 9 & 3707 & 247.68 \\ \hline \end{array}\)

a) Plot the Length of the year against the Distance from the sun. Describe the shape of your plot.

b) Re-express one or both variables to straighten the plot. Use the re-expressed data to create a model describing the length of a planet’s year based on its distance from the sun.

c) Comment on how well your model fits the data.