Question

A certain forest covers an area of 8.25%. Suppose that each year this area decreases by 4800km^2. What will the area be after 5 years?

Answer 1

The area after 5 years is 3120.841 square kilometer

Solution:

The decreasing function is given as:

$y = a(1-r)^t$

Where,

y is future value

a is initial value

r is decreasing rate

t is number of years

From given,

a = 4800

t = 5

$r = 8.25 \% = \frac{8.25}{100} = 0.0825$

Therefore,

$y = 4800(1 - 0.0825)^5\\\\y = 4800 \times 0.9175^5\\\\y = 4800 \times 0.6501\\\\y = 3120.841$

Thus the area after 5 years is 3120.841 square kilometer