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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The differential equation based on the Weber-Fechner Law is $\frac{dr}{ds} = \frac{k}{s}$, where $k$ is a constant of proportionality. Solving this differential equation with the initial condition $r(s_0) = r_0$ leads to the solution $r = r_0 + k \ln\left|\frac{s}{s_0}\right|$.

In Trying to Model the Response to a Stimulus, Psychologists r=s0+kln⁡∣r0r∣r=s_{0}+k \ln \left|\frac{r_{0}}{r}\right|r=s0​+kln​rr0​​​

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