33. If a region's forest cover is decreasing at a rate of 5% per year due to deforestation, and the current forest area is 10,000 square kilometers, what will be the forest area after 10 years assuming no conservation efforts are made?
Key Concept: Renewable Resources, Sustainability
c) 5,987 square kilometers
[Solution Description] The forest area decreases at a rate of 5% per year. This means each year, the forest area is multiplied by 0.95 (since 100% - 5% = 95%). To find the forest area after 10 years, we use the formula for exponential decay: $A = A_0 \times (1 - r)^t$, where $A$ is the final area, $A_0$ is the initial area, $r$ is the annual decrease rate, and $t$ is the number of years. Here, $A_0 = 10,000$, $r = 0.05$, and $t = 10$. Substituting these values, we get $A = 10,000 \times (0.95)^{10}$. Calculating this, $A \approx 10,000 \times 0.5987 \approx 5,987$ square kilometers.
Your Answer is correct.
c) 5,987 square kilometers
[Solution Description] The forest area decreases at a rate of 5% per year. This means each year, the forest area is multiplied by 0.95 (since 100% - 5% = 95%). To find the forest area after 10 years, we use the formula for exponential decay: $A = A_0 \times (1 - r)^t$, where $A$ is the final area, $A_0$ is the initial area, $r$ is the annual decrease rate, and $t$ is the number of years. Here, $A_0 = 10,000$, $r = 0.05$, and $t = 10$. Substituting these values, we get $A = 10,000 \times (0.95)^{10}$. Calculating this, $A \approx 10,000 \times 0.5987 \approx 5,987$ square kilometers.