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.

Step-by-step explanation:

Since we have given that

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

We first consider the equation:

$A=\int\limits^t_0 {8\sqrt{t}} \, dt\\\\A=8\dfrac{t^{\frac{3}{2}}}{\frac{3}{2}}+C\\\\A=\dfrac{16}{3}t^{\frac{3}{2}}+C$

At t=0, A= 2008

So, it becomes,

$2008=C$

So, now it becomes,

$A=\dfrac{16}{3}t^{\frac{3}{2}}+2008\\\\At\ t=24,\\\\A=\dfrac{16}{3}(24)^{\frac{3}{2}}+2008\\\\A=2635.06$

Hence, there are 2635 acres covered 24 hours later.