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

Question

Mathematics

Maxwell Black

6 September, 07:18

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

+3

Answers (1)

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Montana · Answer 1

C. dL/dt=k (100-L)

Step-by-step explanation:

The rate of change of the number of words memorized is proportional to the number of words left to be memorized.

The rate of change is dL/dt.

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)