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The growth of a red oak tree is approximated by the function G=-0.004t3 +0.137t2 + 0.459t-0.824, 2sts 34 where G is the height of the tree (in feet) and t is its age (in years). (a) Use a graphing utility to graph the function. 150 EV 100 50 5 10 15 20 25 30 O G 60 50 40 30 20 10 150 100 G 60 50 40 vh 30 20 10 50 35 5 O t 10 15 20 25 30 35 5 10 15 20 25 30 5 10 15 20 25 30 (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=-0.012t² +0.274t + 0.459. 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=-0.004t3 +0.137t2 + 0.459t-0.824, 2sts 34 where G is the height of the tree (in feet) and t is its age (in years). (a) Use a graphing utility to graph the function. 150 EV 100 50 5 10 15 20 25 30 O G 60 50 40 30 20 10 150 100 G 60 50 40 vh 30 20 10 50 35 5 O t 10 15 20 25 30 35 5 10 15 20 25 30 5 10 15 20 25 30 (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=-0.012t² +0.274t + 0.459. Find the vertex of this parabola. (Round your answer to two decimal places.) (t, y) =

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter3: Linear And Nonlinear Functions
Section3.7: Piecewise And Step Functions
Problem 43PFA
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The growth of a red oak tree is approximated by the function G= -0.004t³ +0.137t2 + 0.459t - 0.824, 2≤t≤ 34 where G is the height of the tree (in feet) and t is its age (in years). Use a graphing utility to graph the function. (a) G 60 40 30 20 5 10 15 20 25 30 35 L vh G 60 50 40 30 20 10 50 10 G 150 100 50 5 10 15 20 25 30 35 t (d) Compare your results from parts (b) and (c). t The t-value of the vertex in part (c) is --Select--- G 150 O 100 50 + 5 10 15 (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 = -0.012t² + 0.274t + 0.459. Find the vertex of this parabola. (Round your answer to two decimal places.) (t, y) = 5 10 15 20 25 30 20 25 30 the value found in part (b).
Transcribed Image Text:The growth of a red oak tree is approximated by the function G= -0.004t³ +0.137t2 + 0.459t - 0.824, 2≤t≤ 34 where G is the height of the tree (in feet) and t is its age (in years). Use a graphing utility to graph the function. (a) G 60 40 30 20 5 10 15 20 25 30 35 L vh G 60 50 40 30 20 10 50 10 G 150 100 50 5 10 15 20 25 30 35 t (d) Compare your results from parts (b) and (c). t The t-value of the vertex in part (c) is --Select--- G 150 O 100 50 + 5 10 15 (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 = -0.012t² + 0.274t + 0.459. Find the vertex of this parabola. (Round your answer to two decimal places.) (t, y) = 5 10 15 20 25 30 20 25 30 the value found in part (b).
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