In 2003, the owl population in a park was measured to be 340...

In $2003,$ the owl population in a park was measured to be $340 .$ By $2007,$ the population was measured again to be $285 .$ If the population continues to change linearly, a. Find a formula for the owl population, $P$. 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 $285 .$ If the population continues to change linearly,
a. Find a formula for the owl population, $P$.
b. What does your model predict the owl population to be in $2012 ?$

Key Concepts

Linear Function Model

A linear function model represents a relationship between two variables by a straight line, typically written in the form y = mx + b, where m is the slope and b is the y-intercept. This model assumes that the change in one variable is proportional to the change in another, making it useful for situations where data changes at a constant rate over time.

Slope

The slope is a measure of the rate of change between two variables, indicating how much the dependent variable changes for a unit change in the independent variable. In the context of linear modeling, it is calculated by the difference in the y-values divided by the difference in the x-values between two data points, and its sign indicates whether the function is increasing or decreasing.

Intercept

The y-intercept in a linear model is the value of the dependent variable when the independent variable is zero. It provides a starting point for the relationship between the variables and is crucial for accurately describing the linear function, especially when the independent variable is translated or shifted relative to the data.

Extrapolation

Extrapolation involves using a linear function beyond the range of observed data to predict future or unknown values. It relies on the assumption that the linear trend established by the known data points continues consistently, allowing the model to forecast outcomes outside of the initial dataset.

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