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

`y=8500(1.12)^(x)`

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.