As an object travels away from a light source, the intensity of the light on the object diminishes. To measure the influence of distance on light intensity, a student uses a light meter to record intensity, in lumens, from a source at various distances. The results, which compare distance in centimeters to the recorded light intensity, are shown in the scatterplot. To develop a linear model, the student next took the log of each distance and the log of each intensity and used computer software to find a least-square equation, shown in the computer output.
Using the computer output, the best estimate of the light intensity at 19 centimeters is:
0.0876, because 0.8561 − 1.4966(log 19) = −1.058, and 10−1.058=0.0876 lumens.
0.3472, because 0.8561 − 1.4966(log 19) = −1.058, and e−1.058=0.3472 lumens.
0.3964, because 0.8561(log 19) − 1.4966 = −0.4018, and 10−0.4018=0.3964 lumens.
0.6691, because 0.8561(log 19) − 1.4966 = −0.4018, and e−0.4018=0.6691 lumens.