• Identify whether a scenario or data describes linear or geometric growth
• Identify key growth parameters, such as growth rates and initial values, and express them in a format that can be used for calculation
• Use equations to predict future values for linear and exponential growth

Understanding Growth Patterns in Real Life

In the real world, understanding growth patterns is crucial for making informed decisions and predictions. From population changes to sales trends, growth can often be categorized as either linear or geometric. In this “Apply It” section, you will encounter a series of scenarios that will challenge you to identify these growth patterns, calculate rates and values, and develop equations to predict future outcomes. Let’s dive into these practical applications to see how the concepts of linear and geometric growth play out in everyday situations.

Scenario 1: Population Growth

The town of Greensville has been experiencing changes in its population. In 2020, the population was [latex]10,000[/latex]. Over the next few years, the population growth was recorded as follows:

• 2021: [latex]10,500[/latex]
• 2022: [latex]11,025[/latex]
• 2023: [latex]11,576[/latex]

Having explored the population dynamics of Greensville, we now turn our attention to the corporate world. XYZ Corporation’s sales revenue provides a different context to apply our understanding of growth patterns. This shift from a demographic to an economic setting will test your ability to adapt and apply mathematical concepts across diverse scenarios.

Scenario 2: Sales Revenue

XYZ Corporation has been tracking its sales revenue over the past few months. The revenue data is as follows:

• Month 1: [latex]$5,000[/latex]
• Month 2: [latex]$6,000[/latex]
• Month 3: [latex]$7,000[/latex]
• Month 4: [latex]$8,000[/latex]