1. Graphing Calculator allowed: On a certain workday, the rate, in tons per hour, at which unprocessed gravel arrives at a gravel processing plant is modeled by G(t) = 90 + 45 cos (+27), where t is measured in hours and 0 ≤t ≤ 8. At the 18. beginning of the workday (t = 0), the plant has 500 tons of unprocessed gravel. During the hours of operation, 0 ≤t ≤ 8, the plant processes gravel at a constant rate of 100 tons per hour. a) Find G'(5). Using correct units, interpret your answer in the context of the problem. b) Find the total amount of unprocessed gravel that arrives at the plant during the hours of operation on this workday. c) Is the amount of unprocessed gravel at the plant increasing or decreasing at time t = 5 hours? Show the work that leads to your answer. d) What is the maximum amount of unprocessed gravel at the plant. during the hours of operation on this workday? Justify your answer.
1. Graphing Calculator allowed: On a certain workday, the rate, in tons per hour, at which unprocessed gravel arrives at a gravel processing plant is modeled by G(t) = 90 + 45 cos (+27), where t is measured in hours and 0 ≤t ≤ 8. At the 18. beginning of the workday (t = 0), the plant has 500 tons of unprocessed gravel. During the hours of operation, 0 ≤t ≤ 8, the plant processes gravel at a constant rate of 100 tons per hour. a) Find G'(5). Using correct units, interpret your answer in the context of the problem. b) Find the total amount of unprocessed gravel that arrives at the plant during the hours of operation on this workday. c) Is the amount of unprocessed gravel at the plant increasing or decreasing at time t = 5 hours? Show the work that leads to your answer. d) What is the maximum amount of unprocessed gravel at the plant. during the hours of operation on this workday? Justify your answer.
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
6th Edition
ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter2: Graphical And Tabular Analysis
Section2.1: Tables And Trends
Problem 1TU: If a coffee filter is dropped, its velocity after t seconds is given by v(t)=4(10.0003t) feet per...
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Transcribed Image Text:1. Graphing Calculator allowed: On a certain workday, the rate, in tons per hour, at
which unprocessed gravel arrives at a gravel processing plant is modeled by
G(t) = 90 + 45 cos (+27), where t is measured in hours and 0 ≤t ≤ 8. At the
18.
beginning of the workday (t = 0), the plant has 500 tons of unprocessed
gravel. During the hours of operation, 0 ≤t ≤ 8, the plant processes gravel at a
constant rate of 100 tons per hour.
a) Find G'(5). Using correct units, interpret your answer in the context of
the problem.
b) Find the total amount of unprocessed gravel that arrives at the plant
during the hours of operation on this workday.
c) Is the amount of unprocessed gravel at the plant increasing or
decreasing at time t = 5 hours? Show the work that leads to your
answer.
d) What is the maximum amount of unprocessed gravel at the plant.
during the hours of operation on this workday? Justify your answer.
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