According to the model, what is the average rate at which passengers board the ship, in passengers per hour, over the time interval 1 ≤ t ≤ 8 hours? b) Write P' (4.5) as the limit of a difference quotient. Use the data in the table to approximate P' (4.5). Show the computations that lead to your answer. c) Must there be a time t, for 3 ≤ t ≤ 6, at which P (t) = 500 ? Justify your answer. d) The total number of gallons of water used by the passengers on the ship is modeled by the function G defined by G (t) = 120t√t for 0 ≤ t ≤ 8, where t is the number of hours since boarding began. Find G' (4), the rate at which passengers use water, in gallons per hour, at time t = 4 hours
According to the model, what is the average rate at which passengers board the ship, in passengers per hour, over the time interval 1 ≤ t ≤ 8 hours? b) Write P' (4.5) as the limit of a difference quotient. Use the data in the table to approximate P' (4.5). Show the computations that lead to your answer. c) Must there be a time t, for 3 ≤ t ≤ 6, at which P (t) = 500 ? Justify your answer. d) The total number of gallons of water used by the passengers on the ship is modeled by the function G defined by G (t) = 120t√t for 0 ≤ t ≤ 8, where t is the number of hours since boarding began. Find G' (4), the rate at which passengers use water, in gallons per hour, at time t = 4 hours
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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a) According to the model, what is the average rate at which passengers board the ship, in passengers per
hour, over the time interval 1 ≤ t ≤ 8 hours?
b) Write P' (4.5) as the limit of a difference quotient. Use the data in the table to approximate P' (4.5).
Show the computations that lead to your answer.
c) Must there be a time t, for 3 ≤ t ≤ 6, at which P (t) = 500 ? Justify your answer.
d) The total number of gallons of water used by the passengers on the ship is modeled by the function G
defined by G (t) = 120t√t for 0 ≤ t ≤ 8, where t is the number of hours since boarding began. Find G' (4),
the rate at which passengers use water, in gallons per hour, at time t = 4 hours.
Transcribed Image Text:t (hours)
P(t) (passengers)
0
0
1
3
35 204
6
600
8
728
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VIEWStep 2: Determine the the average rate at which passengers board the ship, in passengers per hour:
VIEWStep 3: Write P'(4.5) as the limit of a difference quotient
VIEWStep 4: Explain there must be a time for, at which P (t) = 500:
VIEWStep 5: Determine G'(4), the rate at which passengers use water, in gallons per hour, at t=4.
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