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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

Respuesta :

Answer:

D.

[tex]14000=8\times 2^{x+y}[/tex]

Step-by-step 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

[tex]A(x,y)=8(2)^x\times (2)^y[/tex]

now, we can simplify it

[tex]A(x,y)=8(2)^{x+y}[/tex]

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

[tex]14000=8(2)^{x+y}[/tex]

[tex]14000=8\times 2^{x+y}[/tex]

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