Read the instructions for this self-checked activity. Type in your response to each question, and check your answers. At the end of the activity, write a brief evaluation of your work.

Activity
In this activity, you will describe situations that fit given functions and use the functions to solve related problems. Then you will use both functions along with an operation to model a related situation.

Part A
Describe a situation with an output of area in square feet that can be modeled using the function [tex]f(x) = (x)(2x+5)[/tex].



Answer :

### Part A: Situation Description with Area Output in Square Feet

Let's consider a real-world scenario to model the given function [tex]\( f(x) = (x)(2x + 5) \)[/tex].

#### Situation Description

Imagine you have a rectangular garden. The width of this garden is represented by [tex]\( x \)[/tex] feet. The length of this garden, however, is determined by the expression [tex]\( 2x + 5 \)[/tex] feet. This means that the length is always 5 feet more than twice the width.

To find the area of the garden, we use the formula for the area of a rectangle, which is:

[tex]\[ \text{Area} = \text{Width} \times \text{Length} \][/tex]

Given that the width [tex]\( x \)[/tex] and the length [tex]\( 2x + 5 \)[/tex] are defined in feet, the area of the garden can be modeled by the function:

[tex]\[ f(x) = x \cdot (2x + 5) \][/tex]

To summarize, in this situation:
- [tex]\( x \)[/tex] represents the width of the rectangular garden in feet.
- [tex]\( 2x + 5 \)[/tex] represents the length of the garden in feet.
- [tex]\( f(x) = x \cdot (2x + 5) \)[/tex] calculates the area of the garden in square feet.

#### Example Calculations

Let's say the width of the garden ([tex]\( x \)[/tex]) is 3 feet:

1. Calculate the length:
[tex]\[ \text{Length} = 2x + 5 = 2(3) + 5 = 6 + 5 = 11 \text{ feet} \][/tex]

2. Calculate the area using the function [tex]\( f(x) \)[/tex]:
[tex]\[ f(3) = 3 \cdot (2(3) + 5) = 3 \cdot 11 = 33 \text{ square feet} \][/tex]

So, if the width of the garden is 3 feet, the garden's area will be 33 square feet.

### Evaluation of my work

I provided a detailed description of a scenario that fits the given function [tex]\( f(x) = (x)(2x+5) \)[/tex]. By giving a real-world example of a rectangular garden, I effectively demonstrated how the function models the area in square feet. Additionally, I included a specific example calculation to further clarify how the function is applied. I believe my explanation is thorough and should help students grasp the concept and apply the function to similar problems.