Question

There are 24,000 square miles of forest in a western state. Forest fires decrease this area by 9.2% each year. The state needs to have

more than 15,000 square miles of forest to keep their funding from a nonprofit wildlife organization.
Which inequality represents this situation, and if the fires continue to decrease the area of the forests at the same rate, will the state be
able to keep their funding from the nonprofit wildlife organization in 5 years?
O
24,000(1.092) > 15,000; no
0
24,000(0.092) > 15,000; yes
0
24,000(0.908) > 15,000; no
0
24,000(1.098) > 15,000; yes​

Answer 1

24,000(0.908) > 15,000; no

Explanation:

Answer 2

Part 1)
`24,000(0.908)^(5)> 15,000`

Part 2) No

Explanation:

step 1

Let

x ----> the time in years

y ----> the area of the forests is square miles

we know that

The equation that represent this situation is a exponential function of the form

`y=a(b)^(x)`

where

a is the initial value

b is the base

we have

`a=24,000\ mi^(2)`

`b=100\%-9.2\%=90.8\%=90.8/100=0.908`

substitute

`y=24,000(0.908)^(x)`

The inequality that represent the situation is

`24,000(0.908)^(x)> 15,000`

step 2

Verify if the state will be able to keep their funding from the nonprofit wildlife organization in 5 years

For x=5 years

`24,000(0.908)^(5)> 15,000`

`14,813> 15,000` ----> is not true

therefore

The state will be not able to keep their funding from the nonprofit wildlife organization in 5 years