Question

A certain forest covers an area of 3800 km2. Suppose that each year this area decreases by 4.25%. What will the area be after 6 years? Use the calculator provided and round your answer to the nearest square kilometer.

Answer 1

The problem involves a 4.25% yearly decrease in forest area. By repeatedly calculating 95.75% of the remaining forest area, and doing this for six years, we find the area to be approximately 2922 km2 after six years.

Step-by-step explanation:

To calculate the area of the forest after a certain period of time, we need to use the idea of percent decrease, which is a common concept in mathematics.

First, let's understand that a 4.25% decrease each year means the area is actually 100% - 4.25% = 95.75% of its previous size each year. To convert this percentage to a decimal, which we can use in our calculations, we divide by 100 to get 0.9575.

We can use this decimal to calculate the new area each year. Assuming the area of the forest is 3800 km2 initially, after one year the area would be 3800 * 0.9575. After six years, we repeatedly multiply the previous year's area by 0.9575, six times. Using a calculator, we find the area to be about 2922 km^2.

So, if a forest initially covering 3800 km2 decreases in size by 4.25% each year, it will cover approximately 2922 km2 after six years.

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