Modeling Forest Area Decrease

The video tutorial explains how to model the decrease in forest area using an exponential function. Initially, the forest covers 1500 km², decreasing by 7.25% annually. The tutorial introduces variables t (years) and y (forest area) and applies a compound interest formula to derive the exponential function y = 1500 * 0.9275^t, which predicts the forest area over time.

What was the initial area of the forest at the start of the study?

• 2500 km²

• 2000 km²

• 1000 km²

• 1500 km²

By what percentage does the forest area decrease each year?

• 7.25%

• 6.5%

• 8%

• 5%

What happens to the forest area at the start of each new year?

• It increases by 7.25%

• It remains the same

• It doubles

• It decreases by 7.25%

What does the variable 't' represent in the study?

• The initial area of the forest

• The total forest area

• The percentage decrease

• The number of years since the study began

What does the variable 'y' represent in the study?

• The percentage decrease

• The initial area of the forest

• The total forest area

• The number of years since the study began

Which mathematical concept is used to model the decrease in forest area?

• Linear growth

• Quadratic equation

• Simple interest

• Compound interest

What is the purpose of using the compound interest formula in this study?

• To model the annual decrease in forest area

• To calculate the initial forest area

• To determine the annual growth rate

• To find the total forest area after 10 years

What is the initial principal amount in the compound interest formula for this study?

• 2500

• 1500

• 1000

• 2000

How is the annual decrease rate of 7.25% expressed in decimal form?

• 0.0725

• 0.725

• 0.00725

• 7.25

How often is the forest area compounded in the study?

• Monthly

• Biannually

• Quarterly

• Annually