A certain drug is introduced into a person's bloodstream. Suppose that the rate of decrease of the concentration of the drug in the blood is directly proportional to the product of two quantities: (a) the amount of time elapsed since the drug was introduced, and (b) the square of the concentration. Let y = f(t) denote the concentration of the drug in the blood at time t. Set up a differential equation satisfied by f(t). Does the following accurately describe this situation: $y ^ { \prime } = k t y ^ { 2 } , \text { where } k \text { is a negative constant }$

Question

Quizplus · Accepted Answer

The given differential equation $y' = kty^2$ accurately represents the situation where the rate of decrease of the drug concentration ($y'$) is directly proportional to the product of the elapsed time ($t$) and the square of the concentration ($y^2$), with $k$ being a negative constant to indicate the decrease.

A Certain Drug Is Introduced into a Person's Bloodstream y′=kty2, where k is a negative constant y ^ { \prime } = k t y ^ { 2 } , \text { where } k \text { is a negative constant }y′=kty2, where k is a negative constant

A Certain Drug Is Introduced into a Person's Bloodstream $y ^ { \prime } = k t y ^ { 2 } , \text { where } k \text { is a negative constant }$