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^{\box}\\)

Explanation:

Identify the mathematical relationship

Using the Keplers Third Law and Power Regression knowledge points

$$ T^2 = A^3 \implies T = A^{3/2} = A^{1.5} $$

Verify with the given data

Using the Power Regression knowledge point

$$
LATEXBLOCK0
$$

The power regression exponent is \(1.5\) (or \(\frac{3}{2}\)).

Answer:

A power regression equation for this data is:
\(T = A^\wedge\) <blank>\(1.5\)</blank>