A disgruntled pet store owner abandoned an unknown number of...

A disgruntled pet store owner abandoned an unknown number of groundhogs on a small island in 1996 . Since then it has been determined that the average rate of change of the groundhog population was 4 groundhogs per year and that the groundhog population was a linear function of time. When the abandoned groundhogs were discovered in 2001 , there were 376 groundhogs on the island. How many groundhogs did the disgruntled pet store owner originally leave on the island?

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Key Concepts

Average Rate of Change (Slope)

The average rate of change in a linear function is represented by the slope, m. It indicates how much the dependent variable changes for each unit increase in the independent variable. In any linear model, this rate of change is constant, making it straightforward to calculate shifts over time.

Determining the Initial Value

When a linear function is provided with a known rate of change (slope) and a value at a certain time, the initial value can be determined by working backwards. By subtracting the product of the slope and the elapsed time from the known value, the original value at the starting time is found.

Linear Function

A linear function describes a relationship where the rate of change between the two variables remains constant. This means that the function can be expressed in the form f(t) = mt + b, where m is the slope indicating the constant rate of change, and b is the y-intercept or initial value when t is zero or at a specified starting time.

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