Question

Piney Woods Conservation is a company that attempts to help offset the effects of deforestation. A local forest contains approximately 500,000 trees. Lumber companies are continuously clearing the forest at a rate of 4.7% per year. Piney Woods Conservation is about to begin planting trees in the region throughout each year at an average rate of 15,000 trees per year. They are curious to know how long it will be before the number of trees they have planted will be equal to the number of trees still remaining in the forest.

Answer 1

Answer: There is only one solution, and it is viable.

Explanation:

Answer 2

15.7 years

Explanation:

we know that

The deforestation is a exponential function of the form

`y=a(b)^(x)`

where

y ----> the number of trees still remaining in the forest

x ----> the number of years

a is the initial value (a=500,000 threes)

b is the base

b=100%-4.7%=95.3%=95.3/100=0.953

substitute

`y=500,000(0.953)^(x)`

The linear equation of planting threes in the region is equal to

`y=15,000x`

using a graphing tool

Solve the system of equations

The intersection point is (15.7,235,110)

see the attached figure

therefore

For x=15.7 years

The number of trees they have planted will be equal to the number of trees still remaining in the forest