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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) 
(dp)/(ds)=(k)/(p)
(B) 
(dp)/(ds)=(k)/(s)
(C) 
(ds)/(dp)=(k)/(p)
(D) 
(ds)/(dp)=(k)/(s)

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) dpds=kp \frac{d p}{d s}=\frac{k}{p} \newline(B) dpds=ks \frac{d p}{d s}=\frac{k}{s} \newline(C) dsdp=kp \frac{d s}{d p}=\frac{k}{p} \newline(D) dsdp=ks \frac{d s}{d p}=\frac{k}{s}

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) dpds=kp \frac{d p}{d s}=\frac{k}{p} \newline(B) dpds=ks \frac{d p}{d s}=\frac{k}{s} \newline(C) dsdp=kp \frac{d s}{d p}=\frac{k}{p} \newline(D) dsdp=ks \frac{d s}{d p}=\frac{k}{s}
  1. Given Information: We are given that the rate of change of the perceived stimulus pp with respect to the measured intensity ss of the stimulus is inversely proportional to the intensity of the stimulus. This means that as the intensity ss increases, the rate of change of pp decreases, and vice versa. The mathematical way to express an inverse proportionality is by stating that one quantity is equal to a constant divided by the other quantity. In this case, we can write dpds=ks\frac{dp}{ds} = \frac{k}{s}, where kk is a constant of proportionality.
  2. Mathematical Expression: Now we need to match our derived 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 see that option (B) (dpds)=(ks)(\frac{dp}{ds})=(\frac{k}{s}) matches our derived relationship.

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