Explanation Given information: The population denoted by P is P ( t ) = 2.0 × 10 6 + 1000 t 2 and weight per person denoted by Wis W ( t ) = 80 − 0.5 t , where time t is in years. Formula used: The total mass denoted by T ( t ) is the product of population and weight per person. The power rule of differentiation , d d x x n = n x n − 1 . If the second derivative of the function is negative then the function is concave down. If the second derivative of the function is positive then the function is concave up. Calculation: It is provided that the population denoted by P is P ( t ) = 2.0 × 10 6 + 1000 t 2 and weight per person denoted by Wis W ( t ) = 80 − 0.5 t , where time t is in years. Recall that the total mass T ( t ) is the product of population and weight per person. Multiply the functions P ( t ) and W ( t ) . P ( t ) ⋅ W ( t ) = ( 2.0 × 10 6 + 1000 t 2 ) ( 80 − 0.5 t ) T ( t ) = 16.0 × 10 7 − 10 6 t + 8 × 10 4 t 2 − 500 t 3 Differentiate the above expression with respect to t . Recall the power rule of differentiation, d d x x n = n x n − 1 . Apply it, d d t [ T ( t ) ] = d d t [ 16

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

3rd Edition

ISBN: 9780840064189

Author: Frederick R. Adler

Publisher: Cengage Learning

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Chapter 2.7, Problem 37E

To determine

To calculate: The second derivative of the product of the functions P(t)=2.0×106+1000t2 and W(t)=80−0.5t . Verify the result obtained graphically.

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Chapter 2.7, Problem 36E

Chapter 2.7, Problem 38E

Chapter 2 Solutions

Modeling the Dynamics of Life: Calculus and Probability for Life Scientists

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The second derivative of the product of the functions P ( t ) = 2.0 × 10 6 + 1000 t 2 and W ( t ) = 80 − 0.5 t . Verify the result obtained graphically.

Solution Summary: The author calculates the second derivative of the product of functions P(t)=2.0times 106+1000t

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To calculate: The second derivative of the product of the functions P(t)=2.0×106+1000t2 and W(t)=80−0.5t . Verify the result obtained graphically.

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Chapter 2 Solutions