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A certain forest covers an area of 5000 km². Suppose that each year this area decreases by 5%. What will the area be after 10 years?

Use the calculator provided and round your answer to the nearest square kilometer.

User Lifeless
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Answer:

The forest will cover an area of approximately 2994 square kilometers after 10 years.

Explanation:

A forest covers an area of 5000 square kilometers. Each year, the area of the forest decreases by 5%. We want to determine its area after 10 years.

We can write an exponential function to represent the situation. The standard exponential function is given by:


\displaystyle f(x) = a(r)^x

Where a is the initial value, r is the rate, and x is the time that has passed (in this case in years).

Since the original area is 5000 square kilometers, let a = 5000.

Each year, the area decreases by 5%. In other words, for each subsequent year, the forest's area will be 100% - 5% = 95% = 0.95 of its previous year. Hence, r = 0.95.

Thus, our function is:


\displaystyle f(x) = 5000(0.95)^x

Then after 10 years (x = 10), the area will be:


\displaystyle f(10) = 5000(0.95)^((10))= 2993.6846...\approx 2994\text{ km}^2

In conclusion, the forest will cover an area of approximately 2994 square kilometers after 10 years.

User Ivan Khorin
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