ruigE

2021-05-03

In addition to quadratic and exponential models, another common type of model is called a power model. Power models are models in the form $\stackrel{^}{y}=a×{x}^{p}$. Here are data on the eight planets of our solar system. Distance from the sun is measured in astronomical units (AU), the average distance Earth is from the sun.

Use the PwrReg command on your graphing calculator to find a power model relating $y=$ period to $x=$ distance.

Velsenw

Note: The solution gives the commands forthe calculation using a Ti83/84-calculator. If you use a different type of technology, then the commands will differ.
Press on STAT and then select 1:Edit ... Enter the data of distance from the sun in the list L1 and enter the data of period of revolution in the list L2.
Next, press on STAT, select CALC and then select PwrReg. Next; we need to finish the command by entering L1, L2.
PwrReg L1, L2
Finally, pressing on ENTER then gives us the following result:
$y=a\cdot {x}^{b}$
$a=1.0003$
$b=14998$
${r}^{2}=1$
$r=0.9881$
This then implies that the regression line is:
$+y=a\cdot {x}^{b}=10003\cdot {x}^{1.4998}$
where x represents the distance from sun and y represents the period of revulution.

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