https://file.aiquickdraw.com/mathbot/file/1726000404654fqblcmc7.jpg

The question involves determining financial aid using a function that depends on the number of siblings, $ x $, living in the household.

The function is given by:

\[
f(x) = 10000 + 5000x
\]

Where $ x $ is the number of siblings.

You are asked to:
1. Compute $ f(-2) $, $ f(2) $, and $ f(2.5) $.
2. Interpret these values in context.
3. Determine an appropriate domain for the function.

Let's work through the parts:

### Part 1: Calculations

#### a) $ f(-2) $
\[
f(-2) = 10000 + 5000(-2) = 10000 - 10000 = 0
\]
So, $ f(-2) = 0 $.

#### b) $ f(2) $
\[
f(2) = 10000 + 5000(2) = 10000 + 10000 = 20000
\]
So, $ f(2) = 20000 $.

#### c) $ f(2.5) $
\[
f(2.5) = 10000 + 5000(2.5) = 10000 + 12500 = 22500
\]
So, $ f(2.5) = 22500 $.

### Part 2: Interpretation

- $ f(-2) = 0 $: This means that a qualifying applicant with **-2 siblings** in their household would receive \$0 in financial aid. However, having a negative number of siblings does not make sense in this context, so this value is not practical.
  
- $ f(2) = 20000 $: This means that a qualifying applicant with **2 siblings** in their household would receive \$20,000 in financial aid.
  
- $ f(2.5) = 22500 $: This means that a qualifying applicant with **2.5 siblings** (perhaps representing a mixed household where part-time siblings or step-siblings are counted fractionally) would receive \$22,500 in financial aid.

### Part 3: Domain
Since the number of siblings cannot be negative, the appropriate domain for the function should be non-negative numbers, meaning:

\[
\text{Domain: } x \geq 0
\]

Would you like more details about any of these steps? Here are five follow-up questions to extend this discussion:

1. Why does the negative value of $ x $ not make sense in this real-world problem?
2. How would rounding affect the interpretation for fractional values of $ x $?
3. What is the maximum financial aid a student can receive based on this function?
4. How would the function change if the base amount (\$10,000) were higher or lower?
5. Can you think of other variables that could affect financial aid apart from the number of siblings?

**Tip**: When determining the domain of a function in word problems, always consider what makes sense in the real-world context of the problem.

A college has a financial aid formula given by f(x) = 10000 + 5000x, where x is the number of siblings in the household. Compute f(-2), f(2), and f(2.5) and interpret the results. Determine an appropriate domain for the function.

Learn how to calculate financial aid using a linear function f(x) = 10000 + 5000x. This problem covers the real-world application of linear functions and their domain, suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation