students are asked to memorize a list of 100 words. the students are given periodic quizzes to see how many…

students are asked to memorize a list of 100 words. the students are given periodic quizzes to see how many words they have memorized. the function $l$ gives the number of words memorized at time $t$. the rate of change of the number of words memorized is proportional to the number of words left to be memorized. which of the following differential equations could be used to model this situation, where $k$ is a positive constant?\n(a) $\frac{dl}{dt}=kl$\n(b) $\frac{dl}{dt}=100 - kl$\n(c) $\frac{dl}{dt}=k(100 - l)$\n(d) $\frac{dl}{dt}=kl - 100$

students are asked to memorize a list of 100 words. the students are given periodic quizzes to see how many words they have memorized. the function $l$ gives the number of words memorized at time $t$. the rate of change of the number of words memorized is proportional to the number of words left to be memorized. which of the following differential equations could be used to model this situation, where $k$ is a positive constant?\n(a) $\frac{dl}{dt}=kl$\n(b) $\frac{dl}{dt}=100 - kl$\n(c) $\frac{dl}{dt}=k(100 - l)$\n(d) $\frac{dl}{dt}=kl - 100$

Answer

Explanation:

Step1: Identify the rate - of - change and the related quantity

The rate of change of the number of words memorized is $\frac{dL}{dt}$. The total number of words is 100, and the number of words left to be memorized is $100 - L$.

Step2: Set up the proportionality equation

Since the rate of change of the number of words memorized is proportional to the number of words left to be memorized, we have $\frac{dL}{dt}=k(100 - L)$, where $k$ is a positive constant.

Answer:

C. $\frac{dL}{dt}=k(100 - L)$