d. To simplify calculations, a student uses a tangent line approximation to P(t) at 1=0 as a model for the level of pollutants in the lake. At what time t does this model predict that the pollutant levels in the lake will be safe?

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Chapter2: Second-order Linear Odes
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I only need parts d and e answered.

I don't need the answers to parts a, b, or c.

Thank you.

d. To simplify calculations, a student uses a tangent line approximation to P(t) at 1=0 as a model for
the level of pollutants in the lake. At what time t does this model predict that the pollutant levels in
the lake will be safe?
e. Given your answers to parts c and d above, do you feel that the tangent line model is an appropriate
model to use? Explain your reasoning.
Transcribed Image Text:d. To simplify calculations, a student uses a tangent line approximation to P(t) at 1=0 as a model for the level of pollutants in the lake. At what time t does this model predict that the pollutant levels in the lake will be safe? e. Given your answers to parts c and d above, do you feel that the tangent line model is an appropriate model to use? Explain your reasoning.
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).
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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