A puppy gains weight, w, at a rate approximately inversely proportional to its age, t, in months. Which equation describes this relationship? Choose 1 answer: (A) (dw)/(dt)=(k)/(w) (B) (dw)/(dt)=(k)/(t) (C) (dw)/(dt)=kt (D) (dw)/(dt)=kw

Question

A puppy gains weight,  w, at a rate approximately inversely proportional to its age,  t, in months. Which equation describes this relationship? Choose 1 answer: (A)  (dw)/(dt)=(k)/(w) (B)  (dw)/(dt)=(k)/(t) (C)  (dw)/(dt)=kt (D)  (dw)/(dt)=kw

Bytelearn · Accepted Answer

Understand Inverse Proportionality: Understand the concept of inverse proportionality. Inverse proportionality means that as one value increases, the other value decreases at a rate such that their product is constant. In this case, the rate of weight gain (dw/dt) is inversely proportional to the age of the puppy (t). This means that as the puppy gets older (t increases), the rate of weight gain (dw/dt) decreases.Translate into Mathematical Equation: Translate the concept into a mathematical equation. Since the rate of weight gain is inversely proportional to the age, we can express this relationship as (dw/dt) = k/t, where k is a constant of proportionality.Match with Given Choices: Match the equation with the given choices. The equation we derived, (dw/dt) = k/t, matches choice (B) from the given options.

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