Question

A certain forest covers an area of 2300 km^2. Suppose that each year this area decreases by 4%. What will the area be after 12 years?

Round your answer to the nearest square kilometer.

Answer 1

The value of area after 12 years is 1409 square kilometer

Solution:

Given that,

A certain forest covers an area of 2300 square kilometer

Suppose that each year this area decreases by 4%

To find: Area after 12 years

This is decreasing function

The decrease function is given as:

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

Where,

y is the value after t years

A = initial amount

r = decreasing rate in decimal

t is the number of years

Here in this sum,

A = 2300

t = 12 years

`r = 4 \% = (4)/(100) = 0.04`

Substituting the values in formula,

`y = 2300(1-0.04)^(12)\\\\y = 2300(0.96)^(12)\\\\y = 2300 * 0.612709\\\\y = 1409.23 \approx 1409`

Thus value of area after 12 years is 1409 square kilometer