Question

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?

Answer 1

I would assume the following is correct:

y =  (Area of developed land) = (8500 square miles) (1+0.12)^(x)

Answer 2

Answer:

$y=8500(1.12)^{x}$

Step-by-step explanation:

Increase in the population is a phenomenon of exponential growth.

Therefore, growth in the population will lead to the increase in the developed land exponentially.

Function representing the increase in developed land will be $P_{t}=P_{0}r^{t}$

Where $P_{t}$ = Developed land after time 't'

$P_{0}$ = Initial land

t = Time or duration

r = Rate of increase in the developed land

Now we plug in the values in the given function

$P_{0}$ = 8500 square miles

t = x years

$P_{t}$ = y

r = (1 + 12%) = 1.12

$y=8500(1.12)^{x}$ will be the answer.