An apple company owns 6,000 apple trees. Each year the company plans to harvest
10 percentage of its trees and plant 1,000 new trees. Form the difference equation
in π¦π, assuming that number of trees after n years is π¦π and hence solve for π¦π.
Let's denote the number of trees after n years as yn.
After one year, the company harvests 10% of its trees, which is 0.1(6000) = 600 trees. The number of trees after one year is then yn - 600.
After planting 1000 new trees, the total number of trees after one year is yn + 1000 - 600 = yn + 4000.
Therefore, the difference equation is: yn+1 = yn + 4000
Solving the difference equation for yn, we have:
yn = yn-1 + 4000 = yn-2 + 4000 + 4000 = yn-3 + 2(4000) = ... = y0 + n(4000)
yn = 6000 + n(4000)
Therefore, the number of trees after n years is given by yn = 6000 + 4000n.