In 2003 , the owl population in a park was measured to be...

In 2003 , the owl population in a park was measured to be 340. By 2007, the population was measured again to be $285 .$ The population changes linearly. Let the input be years since 1990 . a. Find a formula for the owl population, $P .$ Let the input be years since 2003 . b. What does your model predict the owl population to be in 2012?

In 2003 , the owl population in a park was measured to be 340. By 2007, the population was measured
again to be $285 .$ The population changes linearly. Let the input be years since 1990 .
a. Find a formula for the owl population, $P .$ Let the input be years since 2003 .
b. What does your model predict the owl population to be in 2012?

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Key Concepts

Linear Equation Modeling

This concept involves creating a mathematical representation of a relationship between two variables using a straight-line equation, typically in the form y = mx + b. In modeling population changes, the linear equation expresses how the population changes over time assuming a constant rate of change.

Rate of Change (Slope)

The slope is a measure of how much the dependent variable changes for a unit change in the independent variable. Calculating the slope between two data points allows us to understand the constant rate at which the population increases or decreases over time.

Variable Transformation

Changing the reference point for the independent variable involves shifting the origin of the time scale to simplify calculations or enhance interpretation. This is done by redefining the variable so that calculations are made relative to a more convenient baseline year.

Prediction Using Models

Using a mathematical model created from observed data, predictions for values at future or past time points can be made by substituting the appropriate input into the model. This is a fundamental application of linear equations in forecasting trends based on historical data.

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