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The problem presents a mathematical model using the quadratic function \( f(x) = -4.297x^2 + 72.78x + 97.36 \), which represents the total amount spent by a certain number of people on clothing and footwear from 2000 to 2009. Here, \( x = 0 \) corresponds to January 1, 2000, \( x = 1 \) corresponds to January 1, 2001, and so on. The function \( f(x) \) gives the amount in billions of dollars. The question asks in which year during this period the amount spent was at its maximum, and it requests the final answer to be rounded to the nearest whole number, with intermediate calculations rounded to the nearest tenth. ### Instructions: - Determine the year when spending was at its highest by finding the vertex of the quadratic function. - Enter your calculated result in the provided fields and click "Check Answer." This problem involves applying knowledge of quadratic functions and maxima to interpret real-world spending data within a specified timeframe.

The problem presents a mathematical model using the quadratic function \( f(x) = -4.297x^2 + 72.78x + 97.36 \), which represents the total amount spent by a certain number of people on clothing and footwear from 2000 to 2009. Here, \( x = 0 \) corresponds to January 1, 2000, \( x = 1 \) corresponds to January 1, 2001, and so on. The function \( f(x) \) gives the amount in billions of dollars. The question asks in which year during this period the amount spent was at its maximum, and it requests the final answer to be rounded to the nearest whole number, with intermediate calculations rounded to the nearest tenth. ### Instructions: - Determine the year when spending was at its highest by finding the vertex of the quadratic function. - Enter your calculated result in the provided fields and click "Check Answer." This problem involves applying knowledge of quadratic functions and maxima to interpret real-world spending data within a specified timeframe.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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The problem presents a mathematical model using the quadratic function \( f(x) = -4.297x^2 + 72.78x + 97.36 \), which represents the total amount spent by a certain number of people on clothing and footwear from 2000 to 2009. Here, \( x = 0 \) corresponds to January 1, 2000, \( x = 1 \) corresponds to January 1, 2001, and so on. The function \( f(x) \) gives the amount in billions of dollars. The question asks in which year during this period the amount spent was at its maximum, and it requests the final answer to be rounded to the nearest whole number, with intermediate calculations rounded to the nearest tenth. ### Instructions: - Determine the year when spending was at its highest by finding the vertex of the quadratic function. - Enter your calculated result in the provided fields and click "Check Answer." This problem involves applying knowledge of quadratic functions and maxima to interpret real-world spending data within a specified timeframe.
Transcribed Image Text:The problem presents a mathematical model using the quadratic function \( f(x) = -4.297x^2 + 72.78x + 97.36 \), which represents the total amount spent by a certain number of people on clothing and footwear from 2000 to 2009. Here, \( x = 0 \) corresponds to January 1, 2000, \( x = 1 \) corresponds to January 1, 2001, and so on. The function \( f(x) \) gives the amount in billions of dollars. The question asks in which year during this period the amount spent was at its maximum, and it requests the final answer to be rounded to the nearest whole number, with intermediate calculations rounded to the nearest tenth. ### Instructions: - Determine the year when spending was at its highest by finding the vertex of the quadratic function. - Enter your calculated result in the provided fields and click "Check Answer." This problem involves applying knowledge of quadratic functions and maxima to interpret real-world spending data within a specified timeframe.
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