A 250 lb man starts a diet regimen and loses 1.5 pounds a week. His weight, W, after t weeks can be modeled with the equation:

 

W = 250 - 1.5t

 

What type of model is the equation?

 


A 250 lb man starts a diet regimen and loses 1.5 pounds a week. His weight, W, after t weeks can be modeled with the equation:

 

W = 250 - 1.5t

 

What type of model is the equation?

 


Linear Growth

Linear Decay

Exponential Growth

Exponential Decay


The equation given is:

\[ W = 250 - 1.5t \]

This equation represents a **linear decay** model because the man's weight decreases by a constant amount (1.5 pounds) each week. The slope of -1.5 indicates a consistent, linear decline in weight over time, making it a linear decay model.

So, the correct answer is:

**Linear Decay**

Would you like more details or have any questions?

Here are five related questions:

1. How do we determine if an equation represents growth or decay?
2. What would be the equation for a person gaining 2 pounds per week instead of losing weight?
3. How do we know if a model is linear instead of exponential?
4. What happens to the weight after 10 weeks of this diet regimen according to the equation?
5. Can you explain how the slope affects the rate of weight loss in this linear equation?

**Tip:** In linear models, the slope tells you how fast the quantity changes per unit of time, and the sign (+ or -) shows whether it’s increasing or decreasing.

A 250 lb man starts a diet regimen and loses 1.5 pounds a week. His weight, W, after t weeks can be modeled with the equation: W = 250 - 1.5t. What type of model is the equation? (Linear Growth, Linear Decay, Exponential Growth, Exponential Decay)

Understand how the equation W = 250 - 1.5t models weight loss as a linear decay function. Learn about linear equations, slope, and how weight decreases by a fixed amount each week. This problem is suitable for Grades 8-10 students learning about linear functions.

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