Explanation Given Information: The model to approximate the oxygen consumption t days after the egg was laid is C ( t ) = − 0.0071 t 4 + 0.95 t 3 − 22 t 2 + 95 t ( 25 ≤ t ≤ 50 ) . The time when an egg will typically hatch is t = 50 . The number of newly laid eggs at a time t = 0 is 100 and decreases linearly to zero at t = 50 days. Formula Used: Marginal cost is basically the derivative of the cost function C ( x ) and is defined by C ′ ( x ) . If f ( x ) and g ( x ) are two functions then the product of derivative of functions is, d d x [ f ( x ) ⋅ g ( x ) ] = g ( x ) ⋅ f ′ ( x ) + f ( x ) ⋅ g ′ ( x ) Calculation: Consider the cost function, C ( t ) = − 0.0071 t 4 + 0.95 t 3 − 22 t 2 + 95 t ( 25 ≤ t ≤ 50 ) Evaluate the rate of change of the number of eggs, e g g s = 0 − 100 50 − 0 = − 100 50 = − 2 Evaluate the function for a number of eggs, P ( t ) = m t + b where b is the fixed number and m is the marginal eggs. P ( t ) = − 2 t + 100 Where t is the time. Evaluate the total oxygen consumed. O ( t ) = C ( t ) ⋅ P ( t ) O ( t ) = ( − 0.0071 t 4 + 0.95 t 3 − 22 t 2 + 95 t ) ⋅ ( − 2 t + 100 ) Evaluate the rate of change of total oxygen consumed, O ′ ( t ) O ′ ( t ) = d d t [ C ( t ) ⋅ P ( t ) ] Apply the product rule of derivative, O ′ ( t ) = ( ( − 2 t + 100 ) ⋅ d d t ( − 0.0071 t 4 + 0.95 t 3 − 22 t 2 + 95 t ) + ( − 0.0071 t 4 + 0

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ISBN: 9781337291248

Author: Waner, Stefan.

Publisher: Cengage Learning,

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Chapter 4.3, Problem 94E

To determine

To calculate: The rate of change of total oxygen consumed by embryos after 40 days which is done from the time when the egg is laid through the time the chick hatches where the model to approximate the oxygen consumption t days after the egg was laid for a brush turkey is C(t)=−0.0071t4+0.95t3−22t2+95t (25≤t≤50). The time when an egg will typically hatch is t=50 and the number of newly laid eggs at a time t=0 is 100 and decreases linearly to zero at t=50 days.

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Chapter 4.3, Problem 93E

Chapter 4.3, Problem 95E

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Solution Summary: The author calculates the rate of change of total oxygen consumed by embryos after 40 days. The model to approximate the oxygen consumption t days after the egg was laid for a brush turkey is C(t

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