The number of tons of paper waiting to be recycled at a 24 h recycling plant can be modelled by the equation P(t) where t is the time, in hours, and P(t) is the number of tons waiting to be recycled. a) Use the equation to estimate the instantaneous rate of change in tons of paper waiting to be recycled when this rate is at its maximum. To make = 0.5 sin + 4, your estimate, use each of the following centred intervals: i) Ih before to I h after the time when the instantaneous rate of change is at its maximum ii) 0.5 h before to 0.5 h after the time when the instantaneous rate of change is at its maximum iii) 0.25 h before to 0.25 h after the time when the instantaneous rate of change is at its maximum b) Which estimate is the most accurate? What is the relationship between the size of the interval and the accuracy of the estimate?
The number of tons of paper waiting to be recycled at a 24 h recycling plant can be modelled by the equation P(t) where t is the time, in hours, and P(t) is the number of tons waiting to be recycled. a) Use the equation to estimate the instantaneous rate of change in tons of paper waiting to be recycled when this rate is at its maximum. To make = 0.5 sin + 4, your estimate, use each of the following centred intervals: i) Ih before to I h after the time when the instantaneous rate of change is at its maximum ii) 0.5 h before to 0.5 h after the time when the instantaneous rate of change is at its maximum iii) 0.25 h before to 0.25 h after the time when the instantaneous rate of change is at its maximum b) Which estimate is the most accurate? What is the relationship between the size of the interval and the accuracy of the estimate?
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:The number of tons of paper waiting to be recycled at a 24 h recycling
plant can be modelled by the equation P(t)
where t is the time, in hours, and P(t) is the number of tons waiting to
be recycled.
a) Use the equation to estimate the instantaneous rate of change in tons
of paper waiting to be recycled when this rate is at its maximum. To
make your estimate, use each of the following centred intervals:
i) Ih before to I h after the time when the instantaneous rate of
(등)
E:) + 4,
TT
= 0.5 sin
change is at its maximum
ii) 0.5 h before to 0.5 h after the time when the instantaneous
rate of change is at its maximum
iii) 0.25 h before to 0.25 h after the time when the instantaneous
rate of change is at its maximum
b) Which estimate is the most accurate? What is the relationship
between the size of the interval and the accuracy of the estimate?
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