Answer
(a) $T=d^{1.5}$
(b) Yes.
Work Step by Step
(a) Using technology, we get 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:
$T^2 α d^3$
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.
