Question

orest fire covers 2008 acres at time t equals 0. The fire is growing at a rate of 8 StartRoot t EndRoot acres per hour, where t is in hours. How many acres are covered 24 hours later? Round your answer to the nearest integer.

Answer 1

Answer: There are 2635 acres covered 24 hours later.

Explanation:

Since we have given that

At time t = 0, number of acres forest fire covers = 2008 acres

We first consider the equation:

`A=\int\limits^t_0 {8√(t)} \, dt\\\\A=8\frac{t^{(3)/(2)}}{(3)/(2)}+C\\\\A=(16)/(3)t^{(3)/(2)}+C`

At t=0, A= 2008

So, it becomes,

`2008=C`

So, now it becomes,

`A=(16)/(3)t^{(3)/(2)}+2008\\\\At\ t=24,\\\\A=(16)/(3)(24)^{(3)/(2)}+2008\\\\A=2635.06`

Hence, there are 2635 acres covered 24 hours later.