The shiver-me-Timbers tree farms has 7,800 lumber-quality fast growing trees that are ready to be harvested. The company has a strategy that each year it will harvest 12% of the trees and plant 660 lumber-quality trees during the year. Let n represent the number of years and Yn represent the number of lumber-quality trees on the farm at the end of the year.
The shiver-me-Timbers tree farms has 7,800 lumber-quality fast growing trees that are ready to be harvested. The company has a strategy that each year it will harvest 12% of the trees and plant 660 lumber-quality trees during the year. Let n represent the number of years and Yn represent the number of lumber-quality trees on the farm at the end of the year.
A) Form the difference equation and initial value that models the timber company's strategy where Yn represent the number of lumber-quality trees on the farm at the end of the year and Yn-1 represent the number of lumber-quality trees on the farm at the end of the previous year.
B) solve the difference equation.
C) use the solution of the difference equation to find Y36.
D) Interpret the results for part c.
E) According to the difference equation model, will the tree farm ever reach a point in the future when you have no trees harvest?
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