(1 point) A light, flashing regularly, consists of cycles, each cycle having a d
ID: 3018825 • Letter: #
Question
(1 point) A light, flashing regularly, consists of cycles, each cycle having a dark phase and a light phase. The frequency of this light is measured in cycles per second. As the frequency is increased, the eye initially perceives a series of flashes of light, then a coarse flicker, a fine flicker, and ultimately a steady light. The frequency at which the flickering disappears is called the fusion frequency. The table below shows the results of an experiment in which the fusion frequency F was measured as a function of the light intensityI. 0.8 1.9 4.4 10 21.448.4 92.5218.7437.3 980 F8 12.1 15.2 18.521.7 25.3 28.3 31.9 35.2 38.2 (a) Find a logarithmic model (eg. F = a ln(1) + b ) for the data using the first and last data points in the table. (Round constants to two decimal places) (b) How well does the model in part (a) agree with the actual fusion frequency observed at intensity 218.7? The model predicts a frequency of as compared to the observed frequency of (c) How well does the model in part (a) agree with the observed intensity when determining a fusion frequency of 28.3? The model predicts an intensity of as compared to the observed intensity ofExplanation / Answer
a) F = a ln ( I ) + b
using first and last data point
8 = a ln ( 0.8) + b
8 = -.22314 a + b ------------ equation 1
38.2 = a ln ( 980) + b
38.2 = 6.88755 a + b ------------ equation 2
solving we get
a = 4.25 , b = 8.95
hence, model is
F = 4.25 ln (I ) + 8.95
b) when intensity is 218.7
F = 4.25 ln ( 218.7) + 8.95
F = 31.86
the model predicts a frequency of 31.85 as compared to observed frequency of 31.9
c) when fusion frequncy is 28.3
28.3 = 4.25 ln (I ) + 8.95
I = 94.91
the model predicts an intensity of 94.91 as compared to obesered intensity of 92.5
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