Question

graph the planet data, shown right, using the regression calculator. when you are done, click
esize window to fit data.\ mercury and venus are closer to the sun than earth is. so, their orbital periods are shorter than earths orbit. the further a planet is from the sun, the longer its orbit is. a power regression equation for this data is: t = a^

	mercury	venus	earth	mars	jupiter	saturn	uranus	neptune
t (yr)	0.242	0.616	1	1.88			84.0	165

Explanation:

Step1: Recall Kepler's third - law concept

Kepler's third law states that the square of the orbital period \(T\) of a planet is proportional to the cube of the semi - major axis \(A\) of its orbit, \(T^{2}=kA^{3}\), or in power - regression form \(T = k^{\frac{1}{2}}A^{\frac{3}{2}}\).

Step2: Determine the power - regression equation

Based on the data and the relationship from Kepler's third law, the power - regression equation for the given planet data is \(T = A^{1.5}\).

Answer:

\(T = A^{1.5}\)