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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.

Respuesta :

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:

[tex]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[/tex]

At t=0, A= 2008

So, it becomes,

[tex]2008=C[/tex]

So, now it becomes,

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

Hence, there are 2635 acres covered 24 hours later.

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