Question

A certain forest covers an area of 4000km squared. Suppose that each year this area decreases by 3.75percent. What will the area be after 14 years

Answer 1

After 14 years, the area will be 2342.4 km squared.

Explanation:

Since the area is decreasing, we can use the decaying exponential function

`y = A(1 - r)^(t)`

where

• A represents the initial area.

• r represents the rate at which the area changes

• t is the time period

Given

Initial Area A = 4000 km squared

Rate r = 3.75% = 3.75/100 = 0.0375

Time period t = 14

To Determine

The Area after 14 years = y = ?

Plug in the values in the formula

`y = A(1 - r)^(t)`

`y\:=4000\left(1\:-\:0.0375\right)^(14)`

`y=4000\cdot \:0.9625^(14)`

`y=2342.4` km squared

Therefore, after 14 years, the area will be 2342.4 km squared.