So for this we will be forming an exponential equation, which is y = ab^x, with a = initial value and b = growth/decay.
Since the forest starts off with 2000 km^2, 2000 is our a variable.
Next, since the area is *decreasing* by 4.75%, subtract 0.0475 (4.75% in decimal form) from 1 to get 0.9525. That will be your b variable.
Putting our equation together, its going to be y = 2000(0.9525)^x
Now since time is our independent variable, plug 6 into x and solve:
[tex] y=2000*(0.9525)^6\\ y=1493.55 [/tex]
In short, (rounded to the hundreths) the area will be 1493.55 km^2 in 6 years.
