Due to an increasing population, developed land in a region is increasing at a rate of 12% per year. If there are currently 8,500 square miles of developed land, which equation models the square mileage of developed land, y, after x years?

Question

A.
y = 1.12(8,500)x
B.
y = 8,500(1.12)x
C.
y = 8,500(0.12)x
D.
y = 12(85)x

Answer 1

To model the square mileage of developed land, \( y \), after \( x \) years with an initial amount of \( 8,500 \) square miles and an annual growth rate of \( 12% \), we use the formula for exponential growth:

\[ y = a(1 + r)^x \]

where:

• \( a \) is the initial amount (in this case, \( 8,500 \)),
• \( r \) is the growth rate (as a decimal; for \( 12% \), \( r = 0.12 \)),
• \( x \) is the number of years.

Thus, substituting in the values, we have:

\[ y = 8500(1 + 0.12)^x = 8500(1.12)^x \]

This matches option B:

B. \( y = 8,500(1.12)^x \)

So the correct answer is B.