Question

A forest fire covers twice the amount of forest as it did 3 days ago. If the fire covered 300 square miles 3 days ago and it continues to grow at the same rate, how many square miles will it cover 12 days from now?

Answer 1

1. The fire covered 300
`mi^(2)` 3 days ago

2. Today it covers twice the amount of 3 days ago so 2*300=600 (
`mi^(2)` )

3. After 3 days from today, it will have covered 2*2*300=1200

4. After 3*2=6 days from today, 2*2*2*300=2400

5. After 3*3=9 days from today, 2*2*2*2*300=4800

6. After 3*4=12 days from today, it will have covered 2*2*2*2*2*300=9600 (
`mi^(2)` )

7. We can gereralize: After 3*n days from today, it will have covered
`2^(n+1) *300` (
`mi^(2)` )