Question

A certain forest covers an area of 200km^2. Suppose that each year this area decreases by 8.25%. What will the area be after 12 years?

Answer 1

It's easier if you calculate the percentage of forest that will remain after a year. You get this by taking the "decreased" percentage away from 100:\[100-8.25=91.75\]Then you can figure how much will be left after each year step-by-step:\[1 year - 200 \times 0.9175=183.5\]\[2 years - 183.5 \times 0.9175=168.36125\]etc.
You could take an easier route, and realise that you're just multiplying by 0.9175 every time. You have to do this 12 times. That's the same as multiplying the initial figure by \(0.9175^{12}=0.3559\). What does that get you?