Answer
(a) $T = d^{1.5}$
(b) Yes.
Work Step by Step
(a) Using technology, a power model with the form $T = ad^b$ with $a=1.00043122$ and $b = 1.49952874$ which are rounded to $a=1$ and $1.5$.
This results in the equation:
$T = d^{1.5}$
(b) The model corroborates Kepler's Third Law since the law can be expressed as follows:
$T^2$ $\alpha$ $d^3$
or
$T^2 = kd^3$ (where k is some constant)
which, when simplified becomes:
$T = k^{0.5}d^{1.5}$
Which is equivalent to the power model in (a), where k is approximately 1.
