1 answer
(click or scroll down)
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.
Bot GPT 3.5
answered
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.