A certain chemical vaporizes when exposed to the air. Suppose f(t) is the amount of chemical present. It is found that the rate of vaporization of the chemical is proportional to the amount of chemical present squared. Write a differential equation satisfied by f(t) . Does this equation accurately represent this situation: $\mathrm { y } ^ { \prime } = \mathrm { ky } 2 ; \mathrm { k }

Question

A certain chemical vaporizes when exposed to the air. Suppose f(t) is the amount of chemical present. It is found that the rate of vaporization of the chemical is proportional to the amount of chemical present squared. Write a differential equation satisfied by f(t) . Does this equation accurately represent this situation: $\mathrm { y } ^ { \prime } = \mathrm { ky } 2 ; \mathrm { k } < 0 \text { ? }$

Quizplus · Accepted Answer

The given differential equation $y' = ky^2; k < 0$ accurately represents the situation where the rate of vaporization of the chemical is proportional to the square of the amount of chemical present, with $k < 0$ indicating the amount of chemical decreases over time.

A Certain Chemical Vaporizes When Exposed to the Air y′=ky2;k<0 ? \mathrm { y } ^ { \prime } = \mathrm { ky } 2 ; \mathrm { k } < 0 \text { ? }y′=ky2;k<0 ?

A Certain Chemical Vaporizes When Exposed to the Air $\mathrm { y } ^ { \prime } = \mathrm { ky } 2 ; \mathrm { k } < 0 \text { ? }$