In Trying to Model the Response to a Stimulus, Psychologists $r=s_{0}+k \ln \left|\frac{r_{0}}{r}\right|$

question 108

Multiple Choice

In trying to model the response to a stimulus, psychologists use the Weber Fechner Law.This law states that the rate of change of a response, r, with respect to a stimulus, s, is inversely proportional to the stimulus.Model this law as a differential equation.What is the solution to the differential equation with the initial condition that r(s₀) = r₀ for some initial stimulus, s₀?

• A) \(r=s_{0}+k \ln \left|\frac{r_{0}}{r}\right|\)
• B) \(r=s_{0}+k \ln \left|\frac{r}{r_{0}}\right|\)
• C) \(r=r_{0}+k \ln \left|\frac{s_{0}}{s}\right|\)
• D) \(r=r_{0}+k \ln \left|\frac{s}{s_{0}}\right|\)

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Definitions:

Budget Line

A visual depiction of every potential mix of two products that a consumer can purchase, considering their income and the cost of these items.

Linear Relationship

A direct relationship between two variables that can be represented by a straight line on a graph.

Vertical

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Two-Dimensional Graph

A visualization tool showing the relationship between two variables on a plane, with one variable along the x-axis and the other along the y-axis.