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.