## Calculus 8th Edition

(a) $T = d^{1.5}$ (b) Yes.
(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.