Question

A wildfire is spreading at an alarming rate. The wildfire begins at a size of 8 square feet. It then doubles its width every x hours, and doubles its length every y hours. After a period of time, the wildfire covers 14,000 square feet.

Which equation correctly represents the area of the wildfire in terms of x and y?


A. 14,000 = 16^xy

B. 14,000 = 16xy

C. 14,000 = 8 ⋅ 2^x+y

D. 14,000 = 8 ∗ 2^xy

Answer 1

D.

`14000=8* 2^(x+y)`

Explanation:

The wildfire begins at a size of 8 square feet

It means that initial area =8

It then doubles its width every x hours,

and doubles its length every y hours

so, we can set up equation

`A(x,y)=8(2)^x* (2)^y`

now, we can simplify it

`A(x,y)=8(2)^(x+y)`

we are given

After a period of time, the wildfire covers 14,000 square feet

so, we can set A(x,y)=14000

we get

`14000=8(2)^(x+y)`

`14000=8* 2^(x+y)`