Question

a Forest covers an area of 3900 km squared. suppose that each year this area decreases by 6.25%, what will the area be after 5 years round your answer to the nearest square kilometer

Answer 1

Exponential Decay Function

An exponential decaying function is expressed as:

$C(t)=C_o\cdot(1-r)^t$

Where:

C(t) is the actual value of the function at time t

Co is the initial value of C at t=0

r is the decaying rate, expressed in decimal

The initial area of a forest is Co=3,900 squared km. The rate of decay is r=6.25%, expressed in decimal, r = 6.25/100 = 0.0625

Substituting in the formula:

$C(t)=3,900\cdot(1-0.0625)^t$

Where t is expressed in years. Operating:

$C(t)=3,900\cdot0.9375^t$

After t=5 years, the area of the forest is:

$C(5)=3,900\cdot0.9375^5=3,900\cdot0.7242=2,824$

The above result was rounded to the nearest integer.

The area of the forest will be 2,824 square km after 5 years