A sports enthusiast drinks 2 liters of water per hour. Water is eliminated from the body at a rate proportional to the amount of water in the body (due to perspiration). Write a differential equation satisfied by f(t), the amount of water in the body. Does this equation accurately describe this situation: $\mathrm { y } ^ { \prime } = 2 - \mathrm { ky } ?$

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Quizplus · Accepted Answer

The differential equation $ y' = 2 - ky $ accurately describes the situation because it models the rate of change of water in the body ($y'$) as the difference between the constant intake rate (2 liters per hour) and the elimination rate, which is proportional to the current amount of water in the body ($ky$).

A Sports Enthusiast Drinks 2 Liters of Water Per Hour y′=2−ky?\mathrm { y } ^ { \prime } = 2 - \mathrm { ky } ?y′=2−ky?

A Sports Enthusiast Drinks 2 Liters of Water Per Hour $\mathrm { y } ^ { \prime } = 2 - \mathrm { ky } ?$