How do these models reflect potential career growth paths?

Reflect on the realism of each model in today's job market. Which

model do you think more accurately predicts salary growth, and why?

Consider any external factors that could influence salary growth over time and

how they might fit into these models.

Phase $4$: Presentation

Prepare a presentation of your findings, including graphs, equations, and your

analysis.

Share your conclusions on the implications of linear vs$.$ quadratic salary growth,

supported by your data analysis.

Assessment Criteria:

Accuracy in plotting data and deriving equations.

Depth of analysis in comparing the models.

Critical thinking in discussing the implications of each model.

Clarity and thoroughness in the presentation of findings.

Submission Requirements:

A written report including all calculations, graphs, and analysis.

A PPT file for sharing your findings with the family.

This project aims to not only enhance students' understanding of linear and quadratic

functions but also to apply mathematical reasoning to real$-$world economic issues,

preparing them for complex problem$-$solving in their future academic and professional

endeavors. Inquiry Learning Project: Analyzing Salary Growth Models

Overview:

In this project, students will explore the concepts of linear and quadratic growth as they

apply to salary progression over time. By analyzing given datasets and applying

mathematical models, students will gain insights into how salaries can change and

what factors might influence these changes. This project encourages the application of

mathematical concepts to real$-$world scenarios, fostering a deeper understanding of

both mathematics and economics.

Objective:

To understand and apply linear and quadratic models to salary data.

To analyze and compare the implications of each model on long$-$term salary

progression.

To develop critical thinking and data analysis skills through mathematical

modeling.

Materials Needed:

Spreadsheet software $($e$.$g$.,$ Microsoft Excel, Google Sheets$)$

Desmos Calculator $($optional$)$

Project Phases:

Phase $1$: Define and Understand the Salary Growth Models

Linear Growth Model: Salaries increase by a fixed amount each year.

Quadratic Growth Model: Salaries increase at an accelerating rate, represented by

a quadratic equation.Phase $1$: Define and Understand the Salary Growth Models

$$ Linear Growth Model: Salaries increase by a fixed amount each year.

$$ Quadratic Growth Model: Salaries increase at an accelerating rate, represented by

a quadratic equation.

Phase $2$: Data Analysis and Modeling

Dataset Provided:

$\backslash$table$[[$Year Since Starting Job,Annual Salary $($Linear$),$Annual Salary $($Quadratic$)],[0,$$$40,000,$$$40,000],[1,$$$42,000,$$$42,000],[2,$$$44,000,$$$44,400],[3,$$$46,000,$$$47,200],[4,$$$48,000,$$$50,400],[5,$$$50,000,$$$54,000]]$

Note: The linear model shows a constant growth of $$2,000$ per year. The quadratic model starts with the same base salary and initial increase but then grows at an accelerating rate, which can be represented by a quadratic equation of your derivation based on the given data points.

Tasks:

$1.$Plot both the linear and quadratic salary growth on the same graph using the provided dataset.

Find the linear and quadratic equations based on the given data. For the quadratic equation, determine the coefficients that best fit the provided salary data points using polynomial expressions

Use the equations to predict the salary at the $10$th year of employment for both growth models.

Phase $3$: Comparative Analysis and Reflection

Discuss the implications of each model for long$-$term salary progression.

Consider the following questions:

Which model appears more sustainable for a company in the long run?

$2.$ How do these models reflect potential career growth paths?

$3.$ Reflect on the realism of each model in today$$s job market. Which

model do you think more accurately predicts salary growth, and why?

$$ Consider any external factors that could influence salary growth over time and

how they might fit into these models.

Phase $4$: Presentation

$$ Prepare a presentation of your findings, including graphs, equations, and your

analysis.

$$ Share your conclusions on the implications of linear vs$.$ quadratic salary growth,

supported by your data analysis.