Ch. 3 - Polynomial and Rational Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063당신이 사용하는 게 아니라요?교과서 변경

Lial 13th Edition

Ch. 3 - Polynomial and Rational Functions

문제 7d

4장, 문제 7d

Solve each problem. During the course of a year, the number of volunteers available to run a food bank each month is modeled by $V (x)$ , where $V (x) = 2 x^{2} - 32 x + 150$ between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, $V (x)$ is modeled by $V (x) = 31 x - 226$ . Find the number of volunteers in each of the following months.
October

검증된 단계별 안내

Identify which piece of the piecewise function applies to October. Since October is the 10th month, and the function V(x) = 31x - 226 applies from August (x=8) to December (x=12), use this formula for x = 10.

Substitute x = 10 into the function V(x) = 31x - 226 to set up the expression for the number of volunteers in October.

Write the expression as V(10) = 31 $\times$ 10 - 226.

Simplify the multiplication part first: calculate 31 $\times$ 10.

Subtract 226 from the result of the multiplication to find the number of volunteers in October.

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주요 개념

질문에 올바르게 답하기 위해 반드시 이해해야 하는 핵심 개념들은 다음과 같습니다.

Piecewise Functions

A piecewise function is defined by different expressions depending on the input value's domain. In this problem, V(x) uses one formula from January to August and another from August to December, so understanding how to apply the correct formula based on the month is essential.

Substitution in Functions

Substitution involves replacing the variable in a function with a specific value to find the output. Here, to find the number of volunteers in October, substitute x = 10 into the appropriate piece of the function.

Linear and Quadratic Functions

The problem involves both quadratic (2x² - 32x + 150) and linear (31x - 226) functions. Recognizing the type of function helps in understanding the shape and behavior of the volunteer count over time and correctly evaluating the expressions.

관련 실천

교과서 질문

Use the graph to solve each equation or inequality. Use interval notation where appropriate. 2(x-2) / {(x-1)(x-3)} < 0

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교과서 질문

Solve each problem. During the course of a year, the number of volunteers available to run a food bank each month is modeled by $V (x)$ , where $V (x) = 2 x^{2} - 32 x + 150$ between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, $V (x)$ is modeled by $V (x) = 31 x - 226$ . Find the number of volunteers in each of the following months. Sketch a graph of $y = V (x)$ for January through December. In what month are the fewest volunteers available?

724

views

교과서 질문

Solve each problem. During the course of ayear, the number of volunteers available to run a food bank each month is modeled by $V (x),$ where $V (x) = 2 x^{2} - 32 x + 150$ between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, $V (x)$ is modeled by $V (x) = 31 x - 226$ . Find the number of volunteers in each of the following months.

August

May

December

Solve each problem. During the course of a year, the number of volunteers available to run a food bank each month is modeled by $V (x)$ , where $V (x) = 2 x^{2} - 32 x + 150$ between the months of January and August. Here x is time in months, with x=1 representing January. From August to December, V(x) is modeled by $V (x) = 31 x - 226$ . Find the number of volunteers in each of the following months.

January

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