Write a differential equation describing the given situation: Powdered lemonade dissolves in a pitcher at a rate that is proportional to the amount of undissolved powder remaining.Let P = the total amount of powder added,D = the amount dissolved,and t = time.
A) $\frac { d D } { d t } = k + P - D$
B) $\frac { d D } { d t } = k ( P - D )$
C) $\frac { d D } { d t } = k P ( P - D )$
D) $\frac { d D } { d t } = k P D$

Question

Quizplus · Accepted Answer

The rate of dissolution is proportional to the amount of undissolved powder, which is $P - D$, where $k$ is the proportionality constant.

Write a Differential Equation Describing the Given Situation: Powdered Lemonade dDdt=k+P−D\frac { d D } { d t } = k + P - DdtdD​=k+P−D

Write a Differential Equation Describing the Given Situation: Powdered Lemonade $\frac { d D } { d t } = k + P - D$