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**AP Statistics: Section 4.1 C Power Law Models**

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Power growth can be modeled by the equation _______, where a and b are constants. (Notice that in exponential growth, x is the _________, while in power growth, x is the _____.) exponent base

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We can model power growth using a LSL as follows: Take the ln of both sides. The ln of a product equals the sum of the ln’s. The ln of a power equals the power times the ln.

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Notice that there is a linear relationship between ln y and ln x and that b is the slope of the straight line that links ln y to ln x.

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On July 31, 2005, a team of astronomers announced they had discovered what seemed to be a new planet in our solar system. Xena, the potential planet, is bigger than Pluto and has an average distance from the sun of 9.5 billion miles ( astronomical units). Could Xena be a new planet?

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**Graph the scatterplot of the planetary data. Describe it.**

Positive Curved Strong

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**Graph distance vs. ln (period). Describe it.**

Positive Curved Strong

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**Graph ln (distance) vs. ln (period). Describe it.**

Positive Linear Strong

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**r2 = ________ and the LSL is ____________________________**

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**Plot the residuals. Discuss.**

There is a curved pattern, BUT the residuals are really quite small so we will live with it.

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**Find the prediction equation and predict the period for Xena.**

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