How is the distance from the sun for planets in our solar system related to the mean temperature of each planet? To find out, a scatterplot that relates the natural log of the distance of each planet (including Pluto) from the sun in millions of miles and the natural log of the mean planetary temperature in Kelvin was created. A graph titled l n (Temperature) versus l n (distance) has l n (distance) on the x-axis, and l n (temperature) on the y-axis. Points are in a line with negative slope. A 5-column table with 2 rows. Column 1 is labeled Predictor with entries constant, l n distance. Column 2 is labeled coefficient with entries 7.9009, negative 0.4536. Column 3 is labeled S E Coefficient with entries 0.4381, 0.0706. Column 4 is labeled T with entries 18.03, negative 6.42. Column 5 is labeled P with entries 0.000, 0.004. S = 0.3446, r square = 85.5 percent, r square adjusted = 83.2 percent. Based on the scatterplot and computer output, a reasonable estimate of mean temperature in Kelvin for Saturn, which is 886.7 million miles away from the sun is: 4.822 degrees Kelvin because ŷ = −0.4536(In 886.7) + 7.9009 = 4.822. 124.2 degrees Kelvin because and e4.822 = 124.2. 709.0 degrees Kelvin because and e6.564 = 709.0. 0.05 degrees Kelvin because and e−3.008 = 0.049

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter6: Exponential And Logarithmic Functions

Section: Chapter Questions

Problem 33PT: Enter the data from Table 2 into a graphing calculator and graph the ranking scatter plot. Determine...

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How is the distance from the sun for planets in our solar system related to the mean temperature of each planet? To find out, a scatterplot that relates the natural log of the distance of each planet (including Pluto) from the sun in millions of miles and the natural log of the mean planetary temperature in Kelvin was created. A graph titled l n (Temperature) versus l n (distance) has l n (distance) on the x-axis, and l n (temperature) on the y-axis. Points are in a line with negative slope. A 5-column table with 2 rows. Column 1 is labeled Predictor with entries constant, l n distance. Column 2 is labeled coefficient with entries 7.9009, negative 0.4536. Column 3 is labeled S E Coefficient with entries 0.4381, 0.0706. Column 4 is labeled T with entries 18.03, negative 6.42. Column 5 is labeled P with entries 0.000, 0.004. S = 0.3446, r square = 85.5 percent, r square adjusted = 83.2 percent. Based on the scatterplot and computer output, a reasonable estimate of mean temperature in Kelvin for Saturn, which is 886.7 million miles away from the sun is: 4.822 degrees Kelvin because ŷ = −0.4536(In 886.7) + 7.9009 = 4.822. 124.2 degrees Kelvin because and e4.822 = 124.2. 709.0 degrees Kelvin because and e6.564 = 709.0. 0.05 degrees Kelvin because and e−3.008 = 0.0494.

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