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A native plant species is being re-introduced into a protected site by a team of volunteers, in partnership with a local Indigenous nation. The tribe has relied on this plant for medicinal and cultural uses for millennia, and their relationship with the land ensures that the plant population will stabilize over time. The re-established population t days after the re-introduction project can be (roughly) modeled with the ..004t+.4 60t+6000+3000e. equation P(t) 10e.004t+.4 where P(t) gives an estimated count of the number of individual plants in the area. =

A native plant species is being re-introduced into a protected site by a team of volunteers, in partnership with a local Indigenous nation. The tribe has relied on this plant for medicinal and cultural uses for millennia, and their relationship with the land ensures that the plant population will stabilize over time. The re-established population t days after the re-introduction project can be (roughly) modeled with the ..004t+.4 60t+6000+3000e. equation P(t) 10e.004t+.4 where P(t) gives an estimated count of the number of individual plants in the area. =

Advanced Engineering Mathematics
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 native plant species is being re-introduced into a protected site by a team of volunteers, in partnership with a local Indigenous nation. The tribe has relied on this plant for medicinal and cultural uses for millennia, and their relationship with the land ensures that the plant population will stabilize over time. The re-established population t days after the re-introduction project can be (roughly) modeled with the .004t+.4 60t+6000+3000e. equation P(t) where 10e.004t+.4 P(t) gives an estimated count of the number of individual plants in the area. =
Transcribed Image Text:A native plant species is being re-introduced into a protected site by a team of volunteers, in partnership with a local Indigenous nation. The tribe has relied on this plant for medicinal and cultural uses for millennia, and their relationship with the land ensures that the plant population will stabilize over time. The re-established population t days after the re-introduction project can be (roughly) modeled with the .004t+.4 60t+6000+3000e. equation P(t) where 10e.004t+.4 P(t) gives an estimated count of the number of individual plants in the area. =
Use the graph to estimate how many plants of this species will be in the protected site after the population stabilizes. • Use limits to calculate the eventual stable population size, telling the story of how you choose the computations you do. Was your estimate close? • At what rate is the plant population increasing three weeks (careful with units here) after the re-introduction project? (Again I want to hear your thoughts here!) How does this compare to the rate at which the plant population is growing after ten weeks? What is the rate at which the population is decreasing after two years (again, careful with units)? After three years? • After three years, what is the rate at which the population decrease rate is changing? (Hint: This is related to acceleration. Don't forget to tell the story of how you decide what computations to do here!) ●
Transcribed Image Text:Use the graph to estimate how many plants of this species will be in the protected site after the population stabilizes. • Use limits to calculate the eventual stable population size, telling the story of how you choose the computations you do. Was your estimate close? • At what rate is the plant population increasing three weeks (careful with units here) after the re-introduction project? (Again I want to hear your thoughts here!) How does this compare to the rate at which the plant population is growing after ten weeks? What is the rate at which the population is decreasing after two years (again, careful with units)? After three years? • After three years, what is the rate at which the population decrease rate is changing? (Hint: This is related to acceleration. Don't forget to tell the story of how you decide what computations to do here!) ●
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