Explanation Given: The average price per minute of usage of cellular phone is approximated as, f ( t ) = 31.88 ( 1 + t ) − 0.45 ( 0 ≤ t ≤ 6 ) Where, t is measured in years and t = 0 corresponds to the beginning of 1998. Calculation: Differentiate the function f with respect to t , the expression becomes, f ′ ( t ) = 31.88 [ − 0.45 ( 1 + t ) − 0.45 − 1 d d t ( 1 + t ) ] [ ∵ d d t ( f ( x ) n ) = n f ( x ) n − 1 f ′ ( x ) ] = − 14.34 ( 1 + t ) − 1.45 Thus, the value of f ′ ( t ) is − 14

Applied Calculus for the Managerial, Life, and Social Sciences

10th Edition

ISBN: 9781305887831

Author: Tan

Publisher: CENGAGE CO

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Differential Equations

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Chapter 3, Problem 60RE

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To evaluate: The derivative of the function f(t) , value of the function f′(t) at the beginning of 2000 and the rate of change of function f(t) at the beginning of 2000.

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Chapter 3, Problem 59RE

Chapter 3, Problem 61RE

Chapter 3 Solutions

Applied Calculus for the Managerial, Life, and Social Sciences

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

Ch. 3.1 - Prob. 7E Ch. 3.1 - Prob. 8E Ch. 3.1 - Prob. 9E Ch. 3.1 - Prob. 10E Ch. 3.1 - Prob. 11E Ch. 3.1 - Prob. 12E Ch. 3.1 - Prob. 13E Ch. 3.1 - Prob. 14E Ch. 3.1 - Prob. 15E Ch. 3.1 - Prob. 16E Ch. 3.1 - Prob. 17E Ch. 3.1 - Prob. 18E Ch. 3.1 - Prob. 19E Ch. 3.1 - Prob. 20E Ch. 3.1 - Prob. 21E Ch. 3.1 - Prob. 22E Ch. 3.1 - Prob. 23E Ch. 3.1 - Prob. 24E Ch. 3.1 - Prob. 25E Ch. 3.1 - Prob. 26E Ch. 3.1 - Prob. 27E Ch. 3.1 - Prob. 28E Ch. 3.1 - Prob. 29E Ch. 3.1 - Prob. 30E Ch. 3.1 - Prob. 31E Ch. 3.1 - Prob. 32E Ch. 3.1 - Prob. 33E Ch. 3.1 - Prob. 35E Ch. 3.1 - Prob. 36E Ch. 3.1 - Prob. 37E Ch. 3.1 - Prob. 38E Ch. 3.1 - Prob. 39E Ch. 3.1 - Prob. 40E Ch. 3.1 - Prob. 41E Ch. 3.1 - Prob. 42E Ch. 3.1 - Prob. 43E Ch. 3.1 - Prob. 44E Ch. 3.1 - Prob. 45E Ch. 3.1 - Prob. 46E Ch. 3.1 - Prob. 47E Ch. 3.1 - Prob. 48E Ch. 3.1 - Prob. 49E Ch. 3.1 - Prob. 50E Ch. 3.1 - Prob. 51E Ch. 3.1 - Prob. 52E Ch. 3.1 - Prob. 53E Ch. 3.1 - U.K. MOBILE PHONE VIDEO VIEWERS As mobile phones...Ch. 3.1 - Prob. 55E Ch. 3.1 - Prob. 56E Ch. 3.1 - Prob. 57E Ch. 3.1 - Prob. 58E Ch. 3.1 - Prob. 59E Ch. 3.1 - MOBILE INSTANT MESSAGING ACCOUNTS Mobile instant...Ch. 3.1 - Prob. 61E Ch. 3.1 - Prob. 62E Ch. 3.1 - Prob. 63E Ch. 3.1 - Prob. 64E Ch. 3.1 - Prob. 65E Ch. 3.1 - Prob. 66E Ch. 3.1 - Prob. 67E Ch. 3.1 - Prob. 68E Ch. 3.1 - Prob. 69E Ch. 3.1 - Prob. 70E Ch. 3.1 - Prob. 71E Ch. 3.1 - Prob. 72E Ch. 3.1 - Prob. 73E Ch. 3.1 - Prob. 74E Ch. 3.1 - Prob. 75E Ch. 3.1 - Prob. 76E Ch. 3.1 - Prob. 77E Ch. 3.1 - Prob. 78E Ch. 3.1 - Prob. 1TE Ch. 3.1 - Prob. 2TE Ch. 3.1 - Prob. 3TE Ch. 3.1 - Prob. 4TE Ch. 3.1 - Prob. 5TE Ch. 3.1 - Prob. 6TE Ch. 3.1 - Prob. 7TE Ch. 3.1 - Prob. 8TE Ch. 3.2 - Prob. 1CQ Ch. 3.2 - Prob. 2CQ Ch. 3.2 - Prob. 1E Ch. 3.2 - Prob. 2E Ch. 3.2 - Prob. 3E Ch. 3.2 - Prob. 4E Ch. 3.2 - Prob. 5E Ch. 3.2 - Prob. 6E Ch. 3.2 - Prob. 7E Ch. 3.2 - Prob. 8E Ch. 3.2 - Prob. 9E Ch. 3.2 - Prob. 10E Ch. 3.2 - Prob. 11E Ch. 3.2 - Prob. 12E Ch. 3.2 - Prob. 13E Ch. 3.2 - Prob. 14E Ch. 3.2 - Prob. 15E Ch. 3.2 - Prob. 16E Ch. 3.2 - 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Prob. 28E Ch. 3.4 - Prob. 29E Ch. 3.4 - Prob. 30E Ch. 3.4 - Prob. 31E Ch. 3.4 - Prob. 32E Ch. 3.4 - Prob. 33E Ch. 3.4 - Prob. 34E Ch. 3.4 - Prob. 35E Ch. 3.4 - Prob. 36E Ch. 3.4 - Prob. 37E Ch. 3.4 - Prob. 38E Ch. 3.4 - Prob. 39E Ch. 3.4 - Prob. 40E Ch. 3.4 - Prob. 41E Ch. 3.4 - Prob. 42E Ch. 3.5 - Prob. 1CQ Ch. 3.5 - Prob. 2CQ Ch. 3.5 - Prob. 3CQ Ch. 3.5 - Prob. 4CQ Ch. 3.5 - Prob. 1E Ch. 3.5 - Prob. 2E Ch. 3.5 - Prob. 3E Ch. 3.5 - Prob. 4E Ch. 3.5 - Prob. 5E Ch. 3.5 - Prob. 6E Ch. 3.5 - Prob. 7E Ch. 3.5 - Prob. 8E Ch. 3.5 - Prob. 9E Ch. 3.5 - Prob. 10E Ch. 3.5 - Prob. 11E Ch. 3.5 - Prob. 12E Ch. 3.5 - Prob. 13E Ch. 3.5 - Prob. 14E Ch. 3.5 - Prob. 15E Ch. 3.5 - Prob. 16E Ch. 3.5 - Prob. 17E Ch. 3.5 - Prob. 18E Ch. 3.5 - Prob. 19E Ch. 3.5 - Prob. 20E Ch. 3.5 - Prob. 21E Ch. 3.5 - Prob. 22E Ch. 3.5 - Prob. 23E Ch. 3.5 - Prob. 24E Ch. 3.5 - Prob. 25E Ch. 3.5 - In Exercises 21-28, find the third derivative of...Ch. 3.5 - Prob. 27E Ch. 3.5 - Prob. 28E Ch. 3.5 - Prob. 29E Ch. 3.5 - Prob. 30E Ch. 3.5 - AUTO TRANSMISSIONS .AND FUEL ECONOMY In trying to...Ch. 3.5 - Prob. 32E Ch. 3.5 - Prob. 33E Ch. 3.5 - Prob. 34E Ch. 3.5 - Prob. 35E Ch. 3.5 - Prob. 36E Ch. 3.5 - Prob. 37E Ch. 3.5 - Prob. 38E Ch. 3.5 - Prob. 39E Ch. 3.5 - Prob. 40E Ch. 3.5 - Prob. 41E Ch. 3.5 - Prob. 42E Ch. 3.5 - Prob. 43E Ch. 3.5 - Prob. 44E Ch. 3.5 - Prob. 45E Ch. 3.5 - Prob. 46E Ch. 3.5 - Prob. 47E Ch. 3.5 - Prob. 48E Ch. 3.5 - Prob. 49E Ch. 3.5 - Prob. 50E Ch. 3.5 - Prob. 1TE Ch. 3.5 - Prob. 2TE Ch. 3.5 - Prob. 3TE Ch. 3.5 - Prob. 4TE Ch. 3.5 - In Exercises 1-8, find the value of the second...Ch. 3.5 - Prob. 6TE Ch. 3.5 - Prob. 7TE Ch. 3.5 - Prob. 8TE Ch. 3.6 - Prob. 1CQ Ch. 3.6 - Prob. 2CQ Ch. 3.6 - Prob. 3CQ Ch. 3.6 - Prob. 4CQ Ch. 3.6 - Prob. 1E Ch. 3.6 - Prob. 2E Ch. 3.6 - Prob. 3E Ch. 3.6 - Prob. 4E Ch. 3.6 - Prob. 5E Ch. 3.6 - Prob. 6E Ch. 3.6 - Prob. 7E Ch. 3.6 - Prob. 8E Ch. 3.6 - Prob. 9E Ch. 3.6 - Prob. 10E Ch. 3.6 - Prob. 11E Ch. 3.6 - Prob. 12E Ch. 3.6 - Prob. 13E Ch. 3.6 - Prob. 14E Ch. 3.6 - Prob. 15E Ch. 3.6 - Prob. 16E Ch. 3.6 - Prob. 17E Ch. 3.6 - Prob. 18E Ch. 3.6 - Prob. 19E Ch. 3.6 - Prob. 20E Ch. 3.6 - Prob. 21E Ch. 3.6 - Prob. 22E Ch. 3.6 - Prob. 23E Ch. 3.6 - Prob. 24E Ch. 3.6 - Prob. 25E Ch. 3.6 - Prob. 26E Ch. 3.6 - Prob. 27E Ch. 3.6 - Prob. 28E Ch. 3.6 - Prob. 29E Ch. 3.6 - Prob. 30E Ch. 3.6 - Prob. 31E Ch. 3.6 - Prob. 32E Ch. 3.6 - Prob. 33E Ch. 3.6 - Prob. 34E Ch. 3.6 - Prob. 35E Ch. 3.6 - Prob. 36E Ch. 3.6 - Prob. 37E Ch. 3.6 - Prob. 38E Ch. 3.6 - 39. Volume of a Cylinder The volume of a...Ch. 3.6 - Prob. 40E Ch. 3.6 - Prob. 41E Ch. 3.6 - Prob. 42E Ch. 3.6 - Prob. 43E Ch. 3.6 - Prob. 44E Ch. 3.6 - Prob. 45E Ch. 3.6 - Prob. 46E Ch. 3.6 - Prob. 47E Ch. 3.6 - PRODUCTION FUNCTION FOR A FURNITURE COMPANY The...Ch. 3.6 - Prob. 49E Ch. 3.6 - Prob. 50E Ch. 3.6 - Prob. 51E Ch. 3.6 - Prob. 52E Ch. 3.6 - Prob. 53E Ch. 3.6 - Prob. 54E Ch. 3.6 - Prob. 55E Ch. 3.6 - Prob. 56E Ch. 3.6 - Prob. 57E Ch. 3.6 - Prob. 58E Ch. 3.6 - Prob. 59E Ch. 3.6 - Prob. 60E Ch. 3.6 - Prob. 61E Ch. 3.6 - Prob. 62E Ch. 3.6 - Prob. 63E Ch. 3.6 - Prob. 64E Ch. 3.6 - Prob. 65E Ch. 3.6 - 66. Flow of Water from a Tank Water flows from a...Ch. 3.6 - Prob. 67E Ch. 3.6 - Prob. 68E Ch. 3.6 - Prob. 69E Ch. 3.6 - Prob. 70E Ch. 3.6 - Prob. 71E Ch. 3.6 - Prob. 72E Ch. 3.6 - Prob. 73E Ch. 3.6 - Prob. 74E Ch. 3.7 - Prob. 1CQ Ch. 3.7 - Prob. 2CQ Ch. 3.7 - Prob. 3CQ Ch. 3.7 - Prob. 4CQ Ch. 3.7 - Prob. 1E Ch. 3.7 - Prob. 2E Ch. 3.7 - Prob. 3E Ch. 3.7 - Prob. 4E Ch. 3.7 - Prob. 5E Ch. 3.7 - Prob. 6E Ch. 3.7 - Prob. 7E Ch. 3.7 - Prob. 8E Ch. 3.7 - Prob. 9E Ch. 3.7 - Prob. 10E Ch. 3.7 - Prob. 11E Ch. 3.7 - Prob. 12E Ch. 3.7 - Prob. 13E Ch. 3.7 - Prob. 14E Ch. 3.7 - Prob. 15E Ch. 3.7 - Prob. 16E Ch. 3.7 - Prob. 17E Ch. 3.7 - Prob. 18E Ch. 3.7 - Prob. 19E Ch. 3.7 - Prob. 20E Ch. 3.7 - Prob. 21E Ch. 3.7 - Prob. 22E Ch. 3.7 - Prob. 23E Ch. 3.7 - Prob. 24E Ch. 3.7 - Prob. 25E Ch. 3.7 - Prob. 26E Ch. 3.7 - Prob. 27E Ch. 3.7 - Prob. 28E Ch. 3.7 - Prob. 29E Ch. 3.7 - Prob. 30E Ch. 3.7 - Prob. 31E Ch. 3.7 - Prob. 32E Ch. 3.7 - Prob. 33E Ch. 3.7 - Prob. 34E Ch. 3.7 - Prob. 35E Ch. 3.7 - Prob. 36E Ch. 3.7 - Prob. 37E Ch. 3.7 - Prob. 38E Ch. 3.7 - Prob. 39E Ch. 3.7 - SURFACE AREA OF AN ANIMAL Animal physiologists use...Ch. 3.7 - Prob. 41E Ch. 3.7 - FORECASTING COMMODITY PRICES A certain countrys...Ch. 3.7 - Prob. 43E Ch. 3.7 - Prob. 44E Ch. 3.7 - Prob. 45E Ch. 3.7 - Prob. 46E Ch. 3.7 - Prob. 47E Ch. 3.7 - Prob. 48E Ch. 3.7 - Prob. 49E Ch. 3.7 - In Exercises 49 and 50, determine whether the...Ch. 3.7 - Prob. 1TE Ch. 3.7 - Prob. 2TE Ch. 3.7 - Prob. 3TE Ch. 3.7 - Prob. 4TE Ch. 3.7 - Prob. 5TE Ch. 3.7 - Prob. 6TE Ch. 3.7 - Prob. 7TE Ch. 3.7 - Prob. 8TE Ch. 3 - Prob. 1CRQ Ch. 3 - Prob. 2CRQ Ch. 3 - Prob. 3CRQ Ch. 3 - Prob. 4CRQ Ch. 3 - Prob. 5CRQ Ch. 3 - Prob. 6CRQ Ch. 3 - Prob. 7CRQ Ch. 3 - Prob. 8CRQ Ch. 3 - Prob. 9CRQ Ch. 3 - Prob. 10CRQ Ch. 3 - Prob. 1RE Ch. 3 - Prob. 2RE Ch. 3 - Prob. 3RE Ch. 3 - Prob. 4RE Ch. 3 - Prob. 5RE Ch. 3 - Prob. 6RE Ch. 3 - Prob. 7RE Ch. 3 - Prob. 8RE Ch. 3 - Prob. 9RE Ch. 3 - Prob. 10RE Ch. 3 - Prob. 11RE Ch. 3 - Prob. 12RE Ch. 3 - Prob. 13RE Ch. 3 - Prob. 14RE Ch. 3 - Prob. 15RE Ch. 3 - Prob. 16RE Ch. 3 - Prob. 17RE Ch. 3 - Prob. 18RE Ch. 3 - Prob. 19RE Ch. 3 - Prob. 20RE Ch. 3 - Prob. 21RE Ch. 3 - Prob. 22RE Ch. 3 - Prob. 24RE Ch. 3 - Prob. 25RE Ch. 3 - Prob. 26RE Ch. 3 - Prob. 27RE Ch. 3 - Prob. 28RE Ch. 3 - Prob. 29RE Ch. 3 - Prob. 30RE Ch. 3 - Prob. 31RE Ch. 3 - Prob. 32RE Ch. 3 - Prob. 33RE Ch. 3 - Prob. 34RE Ch. 3 - Prob. 35RE Ch. 3 - Prob. 36RE Ch. 3 - Prob. 37RE Ch. 3 - Prob. 38RE Ch. 3 - Prob. 39RE Ch. 3 - Prob. 40RE Ch. 3 - Prob. 41RE Ch. 3 - Prob. 42RE Ch. 3 - Prob. 43RE Ch. 3 - Prob. 44RE Ch. 3 - Prob. 45RE Ch. 3 - Prob. 46RE Ch. 3 - Prob. 47RE Ch. 3 - Prob. 49RE Ch. 3 - Prob. 50RE Ch. 3 - Prob. 51RE Ch. 3 - Prob. 52RE Ch. 3 - Prob. 53RE Ch. 3 - Prob. 54RE Ch. 3 - Prob. 55RE Ch. 3 - Prob. 56RE Ch. 3 - Prob. 57RE Ch. 3 - Prob. 58RE Ch. 3 - Prob. 59RE Ch. 3 - Prob. 60RE Ch. 3 - Prob. 61RE Ch. 3 - Prob. 62RE Ch. 3 - Prob. 63RE Ch. 3 - Prob. 64RE Ch. 3 - Prob. 65RE Ch. 3 - Prob. 66RE Ch. 3 - Prob. 67RE Ch. 3 - Prob. 68RE Ch. 3 - Prob. 69RE Ch. 3 - Prob. 70RE Ch. 3 - Prob. 71RE Ch. 3 - Prob. 72RE Ch. 3 - Prob. 73RE Ch. 3 - Prob. 74RE Ch. 3 - Prob. 1BM Ch. 3 - Prob. 2BM Ch. 3 - Prob. 3BM Ch. 3 - Prob. 4BM Ch. 3 - Prob. 5BM Ch. 3 - Prob. 6BM

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The derivative of the function f ( t ) , value of the function f ′ ( t ) at the beginning of 2000 and the rate of change of function f ( t ) at the beginning of 2000.

Solution Summary: The author evaluates the derivative of the function f(t), the rate of change, and the average price per minute.

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To evaluate: The derivative of the function f(t) , value of the function f′(t) at the beginning of 2000 and the rate of change of function f(t) at the beginning of 2000.

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Chapter 3 Solutions