If denotes the reaction of the body to some stimulus of
Chapter 3, Problem 3.471(choose chapter or problem)
If denotes the reaction of the body to some stimulus of strength , the sensitivity is defined to be the rate of change of the reaction with respect to . A particular example is that when the brightness of a light source is increased, the eye reacts by decreasing the area of the pupil. The experimental formula has been used to model the dependence of on when is measured in square millimeters and is measured in appropriate units of brightness. (a) Find the sensitivity. ; (b) Illustrate part (a) by graphing both and as functions of . Comment on the values of and at low levels of brightness. Is this what you would expect?
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