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

Answer 1

To model the square mileage of developed land, we can use the formula for exponential growth, which is:

\[ y = y_0(1 + r)^x \]

where:

• \( y_0 \) is the initial amount (current developed land),
• \( r \) is the growth rate (in decimal form),
• \( x \) is the number of years,
• \( y \) is the amount after \( x \) years.

Given:

• The current developed land \( y_0 = 8,500 \) square miles,
• The growth rate \( r = 12% = 0.12 \).

Substituting these values into the formula gives us:

\[ y = 8,500(1 + 0.12)^x \] \[ y = 8,500(1.12)^x \]

From the options provided, the correct equation is:

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