One person owns 7000 trees, and plans to sell 12% of his tree's and plant 600 new ones every year. Will he run out of tree's?(Write a recursive formula that can be used to solve the equation)
no he will not run out of trees rather he will keep selling only 5000 because 12% of 5000 is 600 so he sells 600 trees and he has 4400 and he plants 600 more and it becomes 5000 well basically it keeps goin on, i think the question is related to limits and this could be the formula where x is the number of trees and not the number of years $\displaystyle \frac {88x +60000}{100}$
If $\displaystyle t_n$ is a number of trees the guy has after $\displaystyle n$ years, then the initial condition of the recursive formula is
$\displaystyle t_0 = 7000$
and we can see that
$\displaystyle t_1 = 7000 - 0.12*7000 + 600$
or
$\displaystyle t_1 = t_0 - 0.12*t_0 + 600$
For year n we then have
$\displaystyle t_n = 0.88*t_{n-1} + 600$
This is your recursive formula.
To find out whether he will run out of trees solve this relation and take it's limit when n approaches infinity.
Update:
Made some corrections in the formula.