A forest fire covers 2006 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. the total area covered 24 hours later is entry field with incorrect answer 111811 acres. the tolerance is + / - 2% click if you would like to show work for this question: open show work

Question

Kymani Woodard

Mathematics

30 November, 04:32

A forest fire covers 2006 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. the total area covered 24 hours later is entry field with incorrect answer 111811 acres. the tolerance is + / - 2% click if you would like to show work for this question: open show work

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Paulina Atkinson · Answer 1

Answer: We'll have to integrate the growth rate with respect to time, without forgetting the amount of area covered at the start. A = 2010 + â" 8t1/2 dt (as t goes from 0 to 24) A = 2010 + [ (16/3) t3/2] (as t goes from 0 to 24) A = 2010 + 627 = 2637 acres We don't integrate the 2010 here because whatever effects of the passing of time have already taken place over that area. We just treat it as a constant and add it to the result of integration.