x = number of trees at year n
at year 0, x0 = 7000
at year 1, x1 =.88*X0 + 600 = 6160+600 = 6760
at year 2, x2 = .88*x1 +600 = 6548.8
at year 3 , x3 = .88x2+600 = 6362.9
at year 4, x4 = .88*x3 + 600 = 6199.4
at year 5, x5 = .88*x4+600 = 6055.5
at year 6, x6 = .88*x5+600 = 5928.8
at year 7, x7 = .88*x6+600 = 5817.3
at year 8, x8 = .88*x7+600 = 5719.3
at year 9, x9 = .88*x8+600 = 5633
at year 10,x10= .88*x9+600 = 5557 which is answer to a.
b.
when .12 xn = 600
we lose as many as we gain
xn = 600/.12 = 5000
notice above that we are approaching 5000 as we get to year ten
well, I did part c to explain part b
d. and e.
sure go ahead, but .12 xn = 600 always wins in the long run
The Forever Green Nursery owns 7000 white pine trees. Each year the nursery plans to sell 12% of the trees and to then plant 600 new ones.
a. Find the # of trees owned by the nursery after 10 year
b. Find the # of trees owned by nursery after many years and explain what is occurring
c. What equation can you solve to find the number of trees in the long run
d. Try different starting totals in place of the 7000 trees. Describe any changes to long-run value
e. In the fifth year, a disease destroys many of the nursery's trees. How does the long-run value change?
1 answer
1 answer