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?

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

Answer 1

The answer is C, since there is an increasing amount of land you would add one to .12 and multiply that by the number of years followed by 8500 to get your answer

Answer 2

Answer: C.
`y=8,500(1.12)^x`

Explanation:

The exponential equation with rate of growth r in time period x is given by :-

`y=A(1+r)^x`, where A is the initial value.

Given: The initial area of developed land A= 8,500 square miles

The rate of growth r= 12%=0.12

Now, the equation models the square mileage of developed land, y, after x years will be:

`y=8,500(1+0.12)^x\\\\\Rightarrow\ y=8,500(1.12)^x`