According to Stevens’ Law in psychology, the perceived magnitude of a stimulus is proportional(approximately) to a power of the actual intensity I of the stimulus. Experiments show that the perceivedbrightness B of a light satisfies B = kI2/3, where I is the light intensity, whereas the perceived heaviness Hof a weight W satisfies H = kW3/2 (k is a constant that is different in the two cases). Compute dB/dI anddH/dW and state whether they are increasing or decreasing functions. Then explain the following statements: (a) A 1-unit increase in light intensity is felt more strongly when I is small than when I is large.(b) Adding another pound to a load W is felt more strongly when W is large than when W is small.

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.