Question

A certain forest covers an area of 3800 km². Suppose that each year this area decreases by 3.25%. What will the area be after 11 years?

a) 2385.16 km²

b) 2700.78 km²

c) 3036.21 km²

d) 3411.45 km²

Answer 1

To calculate the forest area after 11 years with a 3.25% annual decrease, the exponential decay formula A = P(1 - r)^t is used. The computed area is approximately 2700.78 km² after 11 years.

Step-by-step explanation:

To calculate the forest area after 11 years, we can use the formula for exponential decay, which represents the decrease in area each year due to deforestation. The area of the forest after t years can be calculated using the formula A = P(1 - r)^t, where A is the area after t years, P is the initial area, and r is the annual rate of decrease.

Given the initial forest area P of 3800 km² and an annual decrease rate r of 3.25% (or 0.0325 when expressed as a decimal), we want to find the area after 11 years (t = 11). Plugging these values into the formula, we get:

A = 3800 × (1 - 0.0325)^11

Using a calculator, we can compute the result:

A = 3800 × (1 - 0.0325)^11= 3800 × (0.9675)^11≈ 2700.78 km²

The forest area after 11 years will be approximately 2700.78 km², which corresponds to option b.