Before current environmental regulations were in place, a certain manufacturing plant released pollutants into a stream that feeds into a small lake. The pollutants in the lake water have been deteriorating over time and are currently changing at a rate that can be modeled by the function P'(t)=1– 3e02di , in gallons/year. A local college professor has been taking her classes to monitor the pollutant levels for the past 5 years. They estimated the pollutant levels to be 50 gallons their first year of collecting data (time t = 0). A level of < 38 gallons is considered safe. a. Show that the pollutants in the lake are currently decreasing (t = 5). b. Use methods of calculus to determine the value of t for which the pollutant levels are at a minimum. c. Use methods of calculus to determine whether the pollutant levels are considered safe at the time you found in part (b).
Before current environmental regulations were in place, a certain manufacturing plant released pollutants into a stream that feeds into a small lake. The pollutants in the lake water have been deteriorating over time and are currently changing at a rate that can be modeled by the function P'(t)=1– 3e02di , in gallons/year. A local college professor has been taking her classes to monitor the pollutant levels for the past 5 years. They estimated the pollutant levels to be 50 gallons their first year of collecting data (time t = 0). A level of < 38 gallons is considered safe. a. Show that the pollutants in the lake are currently decreasing (t = 5). b. Use methods of calculus to determine the value of t for which the pollutant levels are at a minimum. c. Use methods of calculus to determine whether the pollutant levels are considered safe at the time you found in part (b).
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter6: Vector Spaces
Section6.7: Applications
Problem 16EQ
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Transcribed Image Text:Before current environmental regulations were in place, a certain manufacturing plant released pollutants into
a stream that feeds into a small lake. The pollutants in the lake water have been deteriorating over time and
are currently changing at a rate that can be modeled by the function P'(t)=1–3e02di , in gallons/year. A
local college professor has been taking her classes to monitor the pollutant levels for the past 5 years. They
estimated the pollutant levels to be 50 gallons their first year of collecting data (time t = 0). A level of <38
gallons is considered safe.
a. Show that the pollutants in the lake are currently decreasing (t= 5).
b. Use methods of calculus to determine the value of t for which the pollutant levels are at a minimum.
c. Use methods of calculus to determine whether the pollutant levels are considered safe at the time you
found in part (b).
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