standard_description: Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.
problem_activity: The estimated size for a population of rabbits and a population of coyotes in a desert habitat are shown in the table. The estimated population sizes were recorded as a part of a long-term study related to the effect of commercial development on native animal species.
{"table": [{"_attributes": {"class": ["table", "table-bordered"], "style": "width:100%"}, "tbody": [{"tr": [{"td": [{"em": [{"_value": "n"}], "_values": ["Years since initial count (", ")"]}, {"_value": "0"}, {"_value": "3"}, {"_value": "6"}, {"_value": "9"}, {"_value": "12"}, {"_value": "15"}, {"_value": "18"}, {"_value": "21"}, {"_value": "24"}]}, {"td": [{"em": [{"_value": "r"}], "_values": ["Estimated number of rabbits (", ")"]}, {"_value": "14,989"}, {"_value": "10,055"}, {"_value": "5,002"}, {"_value": "10,033"}, {"_value": "15,002"}, {"_value": "10,204"}, {"_value": "4,999"}, {"_value": "10,002"}, {"_value": "14,985"}]}, {"td": [{"em": [{"_value": "c"}], "_values": ["Estimated number of coyotes (", ")"]}, {"_value": "1,995"}, {"_value": "2,201"}, {"_value": "2,003"}, {"_value": "1,795"}, {"_value": "1,999"}, {"_value": "2,208"}, {"_value": "2,010"}, {"_value": "1,804"}, {"_value": "2,001"}]}]}]}]}
Below are sketches of each graph, with a curve fitted to the data.
[IMG]
[IMG]
Write the function for each situation and then calculate the two different numbers of years where the population estimate is about 13,000 for rabbits and 2,100 for coyotes.


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