Answer:
f(x) = 2,000(0.94)^x; 952 km^2
Explanation:
Formula for exponential growth or decay:
f(x) = P(1 + r)^x
where
f(x) = future value in year x
P = present value
r = annual rate of growth (positive) or decrease (negative)
x = time in years
In this problem,
P = 2,000
r = -6% = -0.06; here r is negative since this is a decreasing function
The formula is
f(x) = 2,000(1 - 0.06)^x
f(x) = 2,000(0.94)^x
For year 12, x = 12.
f(x) = 2,000(0.94)^x
f(12) = 2,000(0.94)^12
f(12) = 952