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The rate of change of the perceived stimulus 
p with respect to the measured intensity 
s of the stimulus is inversely proportional to the intensity of the stimulus.
Which equation describes this relationship?
Choose 1 answer:
(A) 
(ds)/(dp)=(k)/(s)
(B) 
(dp)/(ds)=(k)/(s)
(C) 
(dp)/(ds)=(k)/(p)
(D) 
(ds)/(dp)=(k)/(p)

The rate of change of the perceived stimulus p p with respect to the measured intensity s s of the stimulus is inversely proportional to the intensity of the stimulus.\newlineWhich equation describes this relationship?\newlineChoose 11 answer:\newline(A) dsdp=ks \frac{d s}{d p}=\frac{k}{s} \newline(B) dpds=ks \frac{d p}{d s}=\frac{k}{s} \newline(C) dpds=kp \frac{d p}{d s}=\frac{k}{p} \newline(D) dsdp=kp \frac{d s}{d p}=\frac{k}{p}

Full solution

Q. The rate of change of the perceived stimulus p p with respect to the measured intensity s s of the stimulus is inversely proportional to the intensity of the stimulus.\newlineWhich equation describes this relationship?\newlineChoose 11 answer:\newline(A) dsdp=ks \frac{d s}{d p}=\frac{k}{s} \newline(B) dpds=ks \frac{d p}{d s}=\frac{k}{s} \newline(C) dpds=kp \frac{d p}{d s}=\frac{k}{p} \newline(D) dsdp=kp \frac{d s}{d p}=\frac{k}{p}
  1. Define Relationship: The problem states that the rate of change of the perceived stimulus pp with respect to the measured intensity ss is inversely proportional to the intensity ss. This means that as ss increases, the rate of change of pp decreases, and vice versa. The mathematical way to express this is to say that the derivative of pp with respect to ss, dpds\frac{dp}{ds}, is equal to some constant kk divided by the intensity ss. This can be written as ss00.
  2. Match with Options: Now we need to match this relationship with the given options. The correct equation should express dpds\frac{dp}{ds} as being proportional to 1s\frac{1}{s}. Looking at the options, we can see that option (B) dpds=ks\frac{dp}{ds} = \frac{k}{s} matches this description.
  3. Eliminate Incorrect Options: We should check the other options to ensure they do not describe the relationship correctly. Option (A) (dsdp)=ks(\frac{ds}{dp}) = \frac{k}{s} suggests that the rate of change of ss with respect to pp is inversely proportional to ss, which is the inverse of what we are looking for. Option (C) (dpds)=kp(\frac{dp}{ds}) = \frac{k}{p} suggests that the rate of change of pp with respect to ss is inversely proportional to pp, which is not what the problem states. Option (D) (dsdp)=kp(\frac{ds}{dp}) = \frac{k}{p} also does not match the description given in the problem. Therefore, these options can be eliminated.

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