The Shiver-me-Timbers tree farm has 10,000 lumber quality trees ready to be harv

Question

The Shiver-me-Timbers tree farm has 10,000 lumber quality trees ready to be harvested. The company has a strategy of harvesting 12% of the trees (that are remaining at the beginning of the year) and planting 700 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. Do/answer the following: 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. (3 points) B. Solve the difference equation. Show in detail how you arrived at your answer. (5 points) C. Use the solution of the difference equation to find yzs.(2 points) D. Go to page 484 in the textbook and study the information in the "Excel Spreadsheet" segment on how to use the spreadsheet to create a table and graph for a difference equation. Note that the example that the authors show on page 484 is for the difference equation in Example 5 on page 482. Using what you have learned, use Excel to create a table (in columns A and B) for the first 21 values yo to y20) and a graph for the difference equation (and initial value) that you formed in part A above. a. Print out the table (the values in column A and B) and the graph that you produced. (2 points)

Explanation / Answer

Ans - 1:

y(n) = y(n-1)*0;88 + 700

y(0) = 10,000

Ans -2

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Y(z) =0.88*Y(z)/z + 700*z/(z-1)

Y(z) *(z-.88)/z = 700*z/(z-1)

Y(z) = 700*z^2/(z-1)*(z-.88) = k[ z^2/(z-1) - z^2/(z-.88)]

y(n) = k*[u(n+1) + (.88)^(n+1)*u(n+1)]

Ans 3 :

put n =25 in above equation

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