Ch. 3 - Polynomial and Rational Functions

Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook

Lial 13th Edition

Ch. 3 - Polynomial and Rational Functions

Problem 7b

Chapter 4, Problem 7b

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.
May

Verified step by step guidance

Identify the month for which you need to find the number of volunteers. Since May is the 5th month, set $x = 5$.

Determine which piece of the piecewise function applies for $x = 5$. Since May is between January and August, use the function $V(x) = 2x^2 - 32x + 150$.

Substitute $x = 5$ into the function: $V(5) = 2(5)^2 - 32(5) + 150$.

Simplify the expression step-by-step: first calculate \$5^2$, then multiply by 2, then multiply 32 by 5, and finally perform the addition and subtraction.

The result after simplification will give the number of volunteers available in May.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Piecewise Functions

A piecewise function is defined by different expressions over different intervals of the domain. In this problem, V(x) has one formula from January to August and another from August to December. Understanding how to evaluate the correct expression based on the input value x is essential.

Function Evaluation

Function evaluation involves substituting a given input value into the function's formula to find the output. Here, to find the number of volunteers in May (x=5), you substitute 5 into the appropriate expression for V(x) and simplify.

Quadratic Functions

A quadratic function is a polynomial of degree two, typically in the form ax² + bx + c. The first part of V(x) is quadratic, so understanding how to work with quadratic expressions, including substitution and simplification, is necessary to find the number of volunteers.

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Related Practice

Textbook Question

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

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Textbook Question

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

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Textbook Question

Solve each problem. If y varies directly as x, and y=20 when x=4, find y when x = -6.

Textbook Question

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

Textbook Question

December

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Textbook Question

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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