Question

A certain forest covers an area of 3700km^2. Suppose that each year this area decreases by 3.25% . What will the area be after 9 years? round your answer to the nearest square kilometer.

Answer 1

To find the area of the forest after 9 years, we need to calculate the decrease in area each year and subtract it from the original area.

First, let's calculate the decrease in area each year. We know that the area decreases by 3.25% each year, which can be written as 0.0325 in decimal form.

To find the area after 1 year, we multiply the original area by (1 - 0.0325):

3700 km^2 * (1 - 0.0325) = 3578.25 km^2

To find the area after 2 years, we multiply the previous year's area by (1 - 0.0325):

3578.25 km^2 * (1 - 0.0325) = 3460.68 km^2

We continue this process for 9 years, each time multiplying the previous year's area by (1 - 0.0325):

Year 1: 3578.25 km^2

Year 2: 3460.68 km^2

Year 3: 3347.31 km^2

Year 4: 3237.96 km^2

Year 5: 3132.42 km^2

Year 6: 3029.52 km^2

Year 7: 2929.08 km^2

Year 8: 2830.95 km^2

Year 9: 2735.98 km^2

After 9 years, the area of the forest will be approximately 2736 km^2 (rounded to the nearest square kilometer).

Answer 2

decrease 3.25% = 1-(3.25/100)=0.9675

in 9 years the area of ​​the forest will be 3700*0.9675^9=2748.276899..2748km²