A student has 3 hours to cram for an examination and during this time wishes to memorize a set of 60 items. It is said that the rate at which a person can memorize a set of items is proportional to the number of items remaining to be memorized. Thus, if the student memorizes y items in t minutes, dy = k(60 – y) dt where k is a positive constant and y < 60 for all t. Assume that zero items are memorized initially and the student memorizes 15 items in the first 20 minutes. A. Express y as a function of t. B. How many items can the student memorize in 1 hour? in 3 hours?
A student has 3 hours to cram for an examination and during this time wishes to memorize a set of 60 items. It is said that the rate at which a person can memorize a set of items is proportional to the number of items remaining to be memorized. Thus, if the student memorizes y items in t minutes, dy = k(60 – y) dt where k is a positive constant and y < 60 for all t. Assume that zero items are memorized initially and the student memorizes 15 items in the first 20 minutes. A. Express y as a function of t. B. How many items can the student memorize in 1 hour? in 3 hours?
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:A student has 3 hours to cram for an examination and during this time wishes to memorize a set
of 60 items. It is said that the rate at which a person can memorize a set of items is proportional to
the number of items remaining to be memorized. Thus, if the student memorizes y items in t
minutes,
dy
= k(60 – y)
dt
where k is a positive constant and y < 60 for all t. Assume that zero items are memorized initially
and the student memorizes 15 items in the first 20 minutes.
A. Express y as a function of t.
B. How many items can the student memorize in 1 hour? in 3 hours?
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