Cathy is conducting an experiment to measure the relation between a light bulb’s intensity and the distance from the light source. She measures a 100-watt light bulb’s intensity 1 meter from the bulb and at 0.1-meter intervals up to 2 meters from the bulb and obtains the following data.

Physics theory states that the intensity of a light bulb is related to the distance from the light bulb through a power equation.

(a) Draw a scatter diagram treating distance as the explanatory variable.

(b) Determine the logarithm of both the x- and y-values so that X = log x and Y = log y. Draw a scatter diagram of the transformed data.

(c) Find the least-squares regression line of the transformed data.

(d) Find the power equation of best fit.

(e) Use the power equation of best fit to predict the intensity of a 100-watt light bulb that is 2.3 meters away.

Distance Intensity, y Distance Intensity, y (meters),.x (meters),.x 1.0 0.29645 1.6 0.11450 1.1 0.25215 1.7 0.10243 1.2 0.20547 1.8 0.09231 1.3 0.17462 1.9 0.08321 1.4 0.15342 2.0 0.07342 1.5 0.13521