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The growth of a red oak tree is approximated by the function G = -0.003t3 + 0.139t2 + 0.457t - 0.824, 2 ≤ t ≤ 34 where G is the height of the tree (in feet) and t is its age (in years).

The growth of a red oak tree is approximated by the function G = -0.003t3 + 0.139t2 + 0.457t - 0.824, 2 ≤ t ≤ 34 where G is the height of the tree (in feet) and t is its age (in years).

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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Given the function, how can the following problems be solved? 

(b) Estimate the age of the tree when it is growing most rapidly. This point is called the point of diminishing returns because the increase in size will be less with each additional year. (Round your answer to the nearest year.) yr (c) Using calculus, the point of diminishing returns can be found by finding the vertex of the parabola y = -0.009t2 + 0.278t + 0.457. Find the vertex of this parabola. (Round your answer to two decimal places.) (t, y) =
Transcribed Image Text:(b) Estimate the age of the tree when it is growing most rapidly. This point is called the point of diminishing returns because the increase in size will be less with each additional year. (Round your answer to the nearest year.) yr (c) Using calculus, the point of diminishing returns can be found by finding the vertex of the parabola y = -0.009t2 + 0.278t + 0.457. Find the vertex of this parabola. (Round your answer to two decimal places.) (t, y) =
The growth of a red oak tree is approximated by the function G = -0.003t³ + 0.139t2 + 0.457 - 0.824, 2 ≤ t ≤ 34 where G is the height of the tree (in feet) and t is its age (in years).
Transcribed Image Text:The growth of a red oak tree is approximated by the function G = -0.003t³ + 0.139t2 + 0.457 - 0.824, 2 ≤ t ≤ 34 where G is the height of the tree (in feet) and t is its age (in years).
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