. Model in Psychology One problem in psychology is to deter- mine the relation between some physical stimulus and the corresponding sensation or reaction produced in a subject. Suppose that, measured in appropriate units, the strength of a stimulus is s and the intensity of the corresponding sensa- tion is some function of s, say, f(s). Some experimental data suggest that the rate of change of intensity of the sensation with respect to the stimulus is directly proportional to the intensity of the sensation and inversely proportional to the strength of the stimulus; that is, f(s) satisfies the differential equation dy ds for some positive constant k. Solve this differential equation. (Figure 7 shows several solutions corresponding to k = .4.) Strength of stimulus Figure 7 Reaction to stimuli. Intensity of reaction

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Chapter1: Functions And Models
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. Model in Psychology One problem in psychology is to deter-
mine the relation between some physical stimulus and the
corresponding sensation or reaction produced in a subject.
Suppose that, measured in appropriate units, the strength of
a stimulus is s and the intensity of the corresponding sensa-
tion is some function of s, say, f(s). Some experimental data
suggest that the rate of change of intensity of the sensation
with respect to the stimulus is directly proportional to the
intensity of the sensation and inversely proportional to the
strength of the stimulus; that is, f(s) satisfies the differential
equation
dy
ds
for some positive constant k. Solve this differential equation.
(Figure 7 shows several solutions corresponding to k = .4.)
Strength of stimulus
Figure 7 Reaction to stimuli.
Intensity of reaction
Transcribed Image Text:. Model in Psychology One problem in psychology is to deter- mine the relation between some physical stimulus and the corresponding sensation or reaction produced in a subject. Suppose that, measured in appropriate units, the strength of a stimulus is s and the intensity of the corresponding sensa- tion is some function of s, say, f(s). Some experimental data suggest that the rate of change of intensity of the sensation with respect to the stimulus is directly proportional to the intensity of the sensation and inversely proportional to the strength of the stimulus; that is, f(s) satisfies the differential equation dy ds for some positive constant k. Solve this differential equation. (Figure 7 shows several solutions corresponding to k = .4.) Strength of stimulus Figure 7 Reaction to stimuli. Intensity of reaction
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