A small forest contains 4000 trees The new forestry plan is

A small forest contains 4000 trees. The new forestry plan is that each year 20% of the trees will be harvested, and 1000 new trees will be planted. Will the forest disappear? Does it stabilize at a certain number of trees? If so, what number. Explain.

Solution

Since 20 % of 4000 = 800, in the first year, 800 trees will be harvested and 100 new trees will be planted. Thus, at the end of 1st year, the total number of trees is 4000 - 800 + 1000 = 4200 which is higher than 4000. In a similar fashion, the total number of trees will keep increasing each year tiill the number pof trees harvested becomes equal to the total number of trees planted i.e. when stabilization occurs.Let the total number of trees at the time of stabilization be x. Then the number of trees harvested = 20% of x i.e x *20/100 = x/5. Thus, for stabilisation, x/5 = 1000 so that x = 5 * 1000 = 5000. Now, when the total number of trees becomes 5000, 20 % of 5000, i.e. 1000 trees will be harvested and 1000 new trees will be planted so that the total number of trees remains 5000. It will neither exceed 5000 and nor will it go down below this level. Thus, the forest will not disappear. The total number of trees will stabilize at 5000.