a. Explanation Given: The height of growing tree after t years of its plantation is h ( t ) = 0.25 t 2 + 1 , feet. The average height to be found for sample sizes n = 5 , and n = 10 Formula used: Let f ( x ) be a function defined in interval a ≤ x ≤ b , and b − a is divided into “ n ” intervals each of width h given by △ = b − a n , then average value of function for sample size “ n ” is f ¯ = f ( a ) + f ( a + △ ) + f ( a + 2 △ ) + ⋯ f ( a + n − 1 ¯ △ ) n . Calculation: The height of growing tree after t years of its plantation is h ( t ) = 0.25 t 2 + 1 . Thus, growth function for tree is h ( t ) = 0.25 t 2 + 1 feet..... (1) The time interval for growth study is t = 5 years, .e., 0 ≤ t ≤ 5 . Thus, we have a = 0 , b = 5 and n = 5 . Therefore, width of subinterval △ = 5 − 0 5 = 1 year. Hence, the average height of the tree for sample size n = 5 is h ¯ = h ( a ) + h ( a + △ ) + h ( a + 2 △ ) + h ( a + 3 △ ) + h ( a + 4 △ ) n h ¯ = h ( 0 ) + h ( 0 + 1 × 1 ) + h ( 0 + 2 × 1 ) + h ( 0 + 3 × 1 ) + h ( 0 + 4 × 1 ) 5 ⇒ h ¯ = h ( 0 ) + h ( 0 + △ ) + h ( 0 + 2 △ ) + h ( 0 + 3 △ ) + h ( 0 + 4 △ ) 5 ⇒ h ¯ = h ( 0 ) + h ( 1 ) + h ( 2 ) + h ( 3 ) + h ( 4 ) 5 ⇒ h ¯ = ( 0 + 1 ) + ( 0 b. To determine To find : The exact average height of the tree during the first 5 years of its growth. c. To determine To find: The average rate of growth of the tree over the first 5 years.

14th Edition

ISBN: 9781464140051

Author: TAALMAN, Laura, Kohn, Peter

Publisher: W. H. Freeman

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Question

Chapter 4.6, Problem 76A

To determine

To approximate: The average height of tree during first five years using given sample size.

To determine

To find: The exact average height of the tree during the first 5 years of its growth.

To determine

To find: The average rate of growth of the tree over the first 5 years.

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Chapter 4.6, Problem 75A

Chapter 4.6, Problem 77A

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To approximate: The average height of tree during first five years using given sample size .

Solution Summary: The author calculates the average height of the tree during the first five years using a given sample size.

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To approximate: The average height of tree during first five years using given sample size.

To find: The exact average height of the tree during the first 5 years of its growth.

To find: The average rate of growth of the tree over the first 5 years.

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