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A small company has a budget of $1500 to spend on office supplies for its workers. gives the amount that the company can spend on 1500 The function E(x) x each employee. The graph of this function is shown below. -10 100 -90 -80 70 10 0 -10 10 - 70 80 90 100 a. Is it possible for the amount of money per employee to be $0? Explain your reasoning. b. How many employees would the company have if they could afford to spend $25 per employee on office supplies?

A small company has a budget of $1500 to spend on office supplies for its workers. gives the amount that the company can spend on 1500 The function E(x) x each employee. The graph of this function is shown below. -10 100 -90 -80 70 10 0 -10 10 - 70 80 90 100 a. Is it possible for the amount of money per employee to be $0? Explain your reasoning. b. How many employees would the company have if they could afford to spend $25 per employee on office supplies?

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Office Supplies Budget for Employees** A small company has a budget of $1500 to spend on office supplies for its workers. The function \( E(x) = \frac{1500}{x} \) gives the amount that the company can spend on each employee. The graph of this function is shown below. ![Graph depicting the function E(x) = 1500/x] _Explanation of the Graph:_ The graph displays the function \(E(x) = \frac{1500}{x}\), which represents the relationship between the number of employees (x-axis) and the amount spent per employee (y-axis). Key features of the graph: - As the number of employees increases, the amount of money available per employee decreases. - The curve is asymptotic to both the x-axis and the y-axis, meaning it approaches these axes but never actually touches them. _Questions:_ a. **Is it possible for the amount of money per employee to be $0? Explain your reasoning.** No, it is not possible for the amount of money per employee to be $0. As \( x \) (the number of employees) increases, \( \frac{1500}{x} \) gets smaller, but it will never actually reach 0 because \( x \) would have to be infinitely large for \( \frac{1500}{x} \) to equal zero. This is depicted in the graph, where the curve gets infinitely closer to the x-axis but never touches it. b. **How many employees would the company have if they could afford to spend $25 per employee on office supplies?** To find the number of employees when the budget per employee is $25, we set \( E(x) = 25 \) and solve for \( x \): \[ 25 = \frac{1500}{x} \] \[ x = \frac{1500}{25} \] \[ x = 60 \] Therefore, the company would have 60 employees if they could afford to spend $25 per employee on office supplies.
Transcribed Image Text:**Office Supplies Budget for Employees** A small company has a budget of $1500 to spend on office supplies for its workers. The function \( E(x) = \frac{1500}{x} \) gives the amount that the company can spend on each employee. The graph of this function is shown below. ![Graph depicting the function E(x) = 1500/x] _Explanation of the Graph:_ The graph displays the function \(E(x) = \frac{1500}{x}\), which represents the relationship between the number of employees (x-axis) and the amount spent per employee (y-axis). Key features of the graph: - As the number of employees increases, the amount of money available per employee decreases. - The curve is asymptotic to both the x-axis and the y-axis, meaning it approaches these axes but never actually touches them. _Questions:_ a. **Is it possible for the amount of money per employee to be $0? Explain your reasoning.** No, it is not possible for the amount of money per employee to be $0. As \( x \) (the number of employees) increases, \( \frac{1500}{x} \) gets smaller, but it will never actually reach 0 because \( x \) would have to be infinitely large for \( \frac{1500}{x} \) to equal zero. This is depicted in the graph, where the curve gets infinitely closer to the x-axis but never touches it. b. **How many employees would the company have if they could afford to spend $25 per employee on office supplies?** To find the number of employees when the budget per employee is $25, we set \( E(x) = 25 \) and solve for \( x \): \[ 25 = \frac{1500}{x} \] \[ x = \frac{1500}{25} \] \[ x = 60 \] Therefore, the company would have 60 employees if they could afford to spend $25 per employee on office supplies.
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