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juin [17]
3 years ago
5

Students are asked to memorize a list of 100 words. The students are given periodic quizzes to see how many words they have memo

rized. 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
Mathematics
1 answer:
Yuri [45]3 years ago
6 0

Answer:

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)

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The reason is because linear functions always have real solutions while some quadratic functions have only imaginary solutions

Step-by-step explanation:

An asymptote of a curve (function) is the line to which the curve is converging or to which the curve to line distance decreases progressively towards zero as the x and y coordinates of points on the line approaches infinity such that the line and its asymptote do not meet.

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