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

검증된 단계별 안내

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.

비슷한 문제에 대한 검증된 영상 답변:

이 영상 해법은 위 문제에 도움이 된다고 튜터들이 추천한 것입니다.

영상 길이:

도움이 되었나요?

주요 개념

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

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.