This table lists the average distance from the sun to each of the first seven planets, using

Question:

This table lists the average distance from the sun to each of the first seven planets, using Earth's average as a unit.

(a) Plot the number of the planet (Mercury is 1, etc.) versus the distance. It does not look like a line, and so finding the line of best fit is not fruitful.
(b) It does, however look like an exponential curve. Therefore, plot the number of the planet versus the logarithm of the distance. Does this look like a line?
(c) The asteroid belt between Mars and Jupiter is what is left of a planet that broke apart. Renumber so that Jupiter is 6, Saturn is 7, and Uranus is 8, and plot against the log again. Does this look better?
(d) Use least squares on that data to predict the location of Neptune.
(e) Repeat to predict where Pluto is.
(f) Is the formula accurate for Neptune and Pluto? This method was used to help discover Neptune (although the second item is misleading about the history; actually, the discovery of Neptune in position 9 prompted people to look for the "missing planet" in position 5)