Final answer:
The forest area after a 10-year period with a 6.25% annual decline from an initial area of 1900 km² will be calculated using an exponential decay formula. This calculation reflects the challenges faced by global forest habitats diminishing each year, with significant ecological consequences such as loss of biodiversity.
Step-by-step explanation:
The question asks about the decrease in a forest area over time due to deforestation, and it involves calculating the area after a certain percentage decrease per year. Specifically, we are given an initial area of 1900 km² and a decline rate of 6.25% per year, and we're asked to find the area after 10 years.
To solve this, we use the formula for exponential decay: A = Pe^(rt), where:
- A is the amount after time t,
- P is the initial principal balance (initial area in this case),
- r is the rate of decline (expressed as a decimal), and
- t is the time the money is invested (or in this case, the number of years).
In this scenario, P is 1900 km², r is -0.0625 (as a decimal, negative because it is a decrease), and t is 10 years. Plugging these values into the formula gives us:
A = 1900 e^(-0.0625×10)
Performing the calculation, we find that the forest area after 10 years will be approximately:
A = 1900 e^(-0.625)
≈
A
To give more insight into the broader context of the question, research shows that deforestation has significant impacts on wildlife. For example, a typical species-area curve indicates that a reduction in habitat of 90 percent from 100 km² to 10 km² reduces the number of species supported by about 50 percent. This implies that deforestation not only decreases the physical area of forests but also significantly reduces biodiversity.
This mathematical exercise reflects a real-world environmental issue of how deforestation affects forest cover and biodiversity over time.