Question

A forest originally has 10,000 trees. Suppose that the forest naturally replenishes itself by 10 percent per year. That is, at the end of one year, if nothing else happened, it would have 10,000 +(0.10 × 10, 000) = 11, 000 trees. (This assumption is not biologically accurate, but it keeps the math simple). Suppose that 1,500 trees are harvested at the end of each year.

-  How many trees will there be at the end of two years? (Note: Base the 10 percent replenishment amount on the number of trees that exist at the beginning of the second year.)

Answer 1

Initial number of trees=To=10000

Growth rate=g=10%

Number of trees at the end of year 1=T₁=To*(1+g)+1500=10000*(1+10%)+1500=12500

Number of trees at the end of year 2=T₂=T₁*(1+g)+1500=12500*(1+10%)+1500=15250