Skip to main content
Ch. 3 - Polynomial and Rational Functions
Lial - College Algebra 13th Edition
Lial13th EditionCollege AlgebraISBN: 9780136881063Not the one you use?Change textbook
Chapter 4, Problem 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)V(x), where V(x)=2x232x+150V(x)=2x^2-32x+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)V(x) is modeled by V(x)=31x226V(x)=31x-226. Find the number of volunteers in each of the following months.
October

Verified step by step guidance
1
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.

Verified video answer for a similar problem:

This video solution was recommended by our tutors as helpful for the problem above.
Video duration:
3m
Was this helpful?

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 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.
Recommended video:
4:56
Function Composition

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.
Recommended video:
Guided course
5:48
Solving Systems of Equations - Substitution

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.
Recommended video:
05:35
Introduction to Quadratic Equations
Related Practice
Textbook Question

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

502
views
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)V(x), where V(x)=2x232x+150V(x)=2x^2-32x+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)V(x) is modeled by V(x)=31x226V(x)=31x-226. Find the number of volunteers in each of the following months. Sketch a graph of y=V(x)y=V(x) for January through December. In what month are the fewest volunteers available?

724
views
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),V(x), where V(x)=2x232x+150V(x)=2x^2-32x+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)V(x) is modeled by V(x)=31x226V(x)=31x-226. Find the number of volunteers in each of the following months.

August

742
views
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)V(x), where V(x)=2x232x+150V(x)=2x^2-32x+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)V(x) is modeled by V(x)=31x226V(x)=31x-226. Find the number of volunteers in each of the following months.

May

713
views
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)V(x), where V(x)=2x232x+150V(x)=2x^2-32x+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)V(x) is modeled by V(x)=31x226V(x)=31x-226. Find the number of volunteers in each of the following months.

December

517
views
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)V(x), where V(x)=2x232x+150V(x)=2x^2-32x+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)=31x226V(x)=31x-226. Find the number of volunteers in each of the following months.

January

743
views