Explanation Given information: The turtle population is expected grow according to the rule, N ( t ) = 2 t 3 + 3 t 2 − 4 t + 1000 Here, 0 ≤ t ≤ 10 and N ( t ) denotes the population at the end of year t . Calculation: The rate of growth of turtle population is the derivative of the function N ( t ) = 2 t 3 + 3 t 2 − 4 t + 1000 . Differentiate the function N ( t ) with respect to t . N ′ ( t ) = d d t ( 2 t 3 + 3 t 2 − 4 t + 1000 ) = d d t 2 t 3 + d d t 3 t 2 − d d t 4 t + d d t 1000 ( d d x [ f ( x ) ± g ( x ) ] = d d x [ f ( x ) ] ± d d x [ g ( x ) ] ) = 2 d d t t 3 + 3 d d t t 2 − 4 d d t t + 0 ( d d x [ c f ( x ) ] = c d d x [ f ( x ) ] ) = 2 ( 3 t 3 − 1 ) + 3 ( 2 t 2 − 1 ) − 4 ( 1 t 1 − 1 ) ( d d x ( x ) n = n x n − 1 ) Simplify it further. N ′ ( t ) = 2 ( 3 t 2 ) + 3 ( 2 t ) − 4 ( t 0 ) = 6 t 2 + 6 t − 4 Substitute 2 for t in N ′ ( t ) = 6 t 2 + 6 t − 4 to calculate the rate of growth of turtle population when t = 2

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

10th Edition

ISBN: 9781305657861

Author: Soo T. Tan

Publisher: Cengage Learning

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Chapter 3.1, Problem 66E

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The rate of growth of turtle population when t=2 and t=8 , and the population of the turtles 10 years after the implementation of the conservation measures.

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Chapter 3.1, Problem 65E

Chapter 3.1, Problem 67E

Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences (MindTap Course List)

Ch. 3.1 - State the following rules of differentiation in...Ch. 3.1 - Prob. 2CQ Ch. 3.1 - Prob. 3CQ Ch. 3.1 - Prob. 4CQ Ch. 3.1 - Prob. 1E Ch. 3.1 - Prob. 2E Ch. 3.1 - Prob. 3E Ch. 3.1 - Prob. 4E Ch. 3.1 - Prob. 5E Ch. 3.1 - Prob. 6E

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The rate of growth of turtle population when t = 2 and t = 8 , and the population of the turtles 10 years after the implementation of the conservation measures.

Solution Summary: The author calculates the rate of growth of turtle population according to the function N(t) with respect to t.

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The rate of growth of turtle population when t=2 and t=8 , and the population of the turtles 10 years after the implementation of the conservation measures.

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