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?
A. dL/dt=kL
B. dL/dt=100−kL
C. dL/dt=k(100−L)
D. dL/dt=kL−100

The rate is a constant k. Since the rate is proportional to the number of words left to be memorized, and the initial number of words is 100, k has to be multiplied by (100-L).

So the correct answer is:

C. dL/dt=k(100−L)

ahirohit963 ahirohit963 · Answer 2 · 2021-11-20T08:38:07+01:00

The differential equations that could be used to model the given situation is [tex]\rm \dfrac{dL}{dt}\;=K (100-L)[/tex] where k is a positive constant where dL/dt is the rate of change of the number of words memorized, and (100 - L) is the number of words left to be memorized.

Given :

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.

According to the given data, the rate of change of the number of words memorized is proportional to the number of words left to be memorized.

The mathematical expression of the above statement is given below:

[tex]\rm \dfrac{dL}{dt}\;\alpha \;(100-L)[/tex]

where dL/dt is the rate of change of the number of words memorized, and (100 - L) is the number of words left to be memorized.

Now, the above expression becomes:

[tex]\rm \dfrac{dL}{dt}\;=K (100-L)[/tex]

where k is proportionality constant.

So, the correct option is D).

For more information, refer to the link given below:

https://brainly.com/question/17921485