Explanation Given Information: The provided function is I ( t ) = 0.5532 t 2 + 738.5 t + 34 , 430 . Formula used: The base of the rectangles to approximate the area is b − a n where the interval [ a , b ] on which function is defined is divided into n subintervals. The height of the rectangles is the value of the function calculated at the right-hand end point of the interval containing the base. The area of a rectangle is b a s e × h e i g h t . The approximated area under the curve is sum of the areas of each rectangle. Calculation: Consider the function, I ( t ) = 0.5532 t 2 + 738.5 t + 34 , 430 The domain on which function is defined is [ 8 , 13 ] . Divide the interval [ 8 , 13 ] into n = 10 subintervals where the function is evaluated at right end points of the subintervals. The base of the rectangles to approximate the area is b − a n where the interval [ a , b ] on which function is defined is divided into n subintervals. Since, the function is defined from t = 8 to t = 13 . So, a = 8 and b = 13 . Thus, Base of each rectangle = 13 − 8 10 = 5 10 = 0.5 Recall that the height of the rectangles is the value of the function calculated at the right-hand end point of the interval containing the base. Record these values in a table. Rectangle Base Right endpoint Height A r e a = b a s e × h e i g h t [ 8 , 8.5 ] 0.5 x 1 = 8.5 I ( 8.5 ) = 0.5532 ( 8.5 ) 2 + 738.5 ( 8.5 ) + 34 , 430 = 40747.2187 0.5 × 40747.2187 [ 8.5 , 9 ] 0.5 x 2 = 9 I ( 9 ) = 0.5532 ( 9 ) 2 + 738.5 ( 9 ) + 34 , 430 = 41121.3092 0.5 × 41121.3092 [ 9 , 9.5 ] 0.5 x 3 = 9.5 I ( 9.5 ) = 0.5532 ( 9.5 ) 2 + 738.5 ( 9.5 ) + 34 , 430 = 41495.6763 0.5 × 41495.6763 [ 9.5 , 10 ] 0.5 x 4 = 10 I ( 10 ) = 0.5532 ( 10 ) 2 + 738.5 ( 10 ) + 34 , 430 = 41870.32 0.5 × 41870.32 [ 10 , 10.5 ] 0.5 x 5 = 10

Mathematical Applications for the Management, Life, and Social Sciences

12th Edition

ISBN: 9781337625340

Author: Ronald J. Harshbarger, James J. Reynolds

Publisher: Cengage Learning

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Chapter 13.1, Problem 40E

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To calculate: The area under the graph of I(t)=0.5532t2+738.5t+34,430 between t=8 and t=13 using n=10 equal subdivisions measured at the right-handend points and what does this area represent where the function I(t)=0.5532t2+738.5t+34,430 represents per capita personal disposable income.

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Chapter 13.1, Problem 39E

Chapter 13.2, Problem 1CP

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Chapter 13 Solutions

Mathematical Applications for the Management, Life, and Social Sciences

Ch. 13.1 - CHECKPOINT 1. For the interval [0, 2]. determine...Ch. 13.1 - Prob. 2CP Ch. 13.1 - Prob. 1E Ch. 13.1 - Prob. 2E Ch. 13.1 - Prob. 3E Ch. 13.1 - Prob. 4E Ch. 13.1 - Prob. 5E Ch. 13.1 - Prob. 6E Ch. 13.1 - Prob. 7E Ch. 13.1 - Prob. 8E

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Solution Summary: The author calculates the area under the graph of I(t) = 212,170 dollars using n=10 equal subdivisions measured at the right-handend points.

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To calculate: The area under the graph of I(t)=0.5532t2+738.5t+34,430 between t=8 and t=13 using n=10 equal subdivisions measured at the right-handend points and what does this area represent where the function I(t)=0.5532t2+738.5t+34,430 represents per capita personal disposable income.

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Chapter 13 Solutions