116k views
4 votes
a forest fire covers 2000 acres at time t=0. the fire is growing at a rate of 8t? acres per hour, where t is in hours. how many acres are covered 24 hours later?

User Cusejuice
by
8.1k points

1 Answer

1 vote

Certainly! Here's how we can solve it:

The initial area that a forest fire covers at time t=0 is 2000 acres.

The fire then grows at an hourly rate. This rate is 8t² acres per hour, where t is the time in hours.

To find how many acres are covered 24 hours later, we would substitute t = 24 into the formula for the fire's growth rate. So we would calculate the number of acres covered in 24 hours as follows:

Area covered = Initial area + Growth of area

We've been told that the initial area is 2000 acres and the growth of the area is calculated by the formula 8t².

Substituting t=24 hours into the formula gives 8*(24²) which equals 4608 acres. This is the growth of the area after 24 hours.

The total area is therefore 2000 acres (initial area) + 4608 acres (growth) = 6608 acres.

Thus, 6608 acres are covered 24 hours later.

User McGiogen
by
7.4k points

No related questions found