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Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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4. Find the equation of the tangent line to the graph of f (x) at this point, telling me the story of your process. 5. Use the equation of the tangent line to estimate the tree population when the beetle population is 30,000, telling me the story of your process.
Transcribed Image Text:4. Find the equation of the tangent line to the graph of f (x) at this point, telling me the story of your process. 5. Use the equation of the tangent line to estimate the tree population when the beetle population is 30,000, telling me the story of your process.
A team of researchers finds that there is a relationship between the overall health of a forest they're studying and the population of a certain beetle which feeds on the bark of old-growth trees. Due to the warming climate, the beetles are now able to reproduce one more time per year than they previously did, exacerbating the stress caused by the drought of the past few seasons. 13x³+67 They use the function f (x) = to model .6x5+39 the relationship between the two populations, where x is in tens of thousands of beetles and f is in thousands of trees. They note that there is a beneficial contribution to the ecosystem as a whole for a smaller population of the beetles, but that the number of healthy trees sharply declines as the beetle population rises too much.
Transcribed Image Text:A team of researchers finds that there is a relationship between the overall health of a forest they're studying and the population of a certain beetle which feeds on the bark of old-growth trees. Due to the warming climate, the beetles are now able to reproduce one more time per year than they previously did, exacerbating the stress caused by the drought of the past few seasons. 13x³+67 They use the function f (x) = to model .6x5+39 the relationship between the two populations, where x is in tens of thousands of beetles and f is in thousands of trees. They note that there is a beneficial contribution to the ecosystem as a whole for a smaller population of the beetles, but that the number of healthy trees sharply declines as the beetle population rises too much.
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