Let the population of rabbits surviving at a time t be governed by the differential equation d p t d t = 1 2 { p t - 400 } . If p ( 0 ) = 100 , then p ( t ) equals

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Aicharya · Accepted Answer

d p t d t = 1 2 { p t - 400 } p 0 = 100 2 d p t p t - 400 = d t Integrating, &#8658; &#8747; 0 p ( t ) dp ( t ) p t - 400 = &#8747; 0 t 1 2 dt &#8658; ln p t - 400 0 p t = t 2 &#8658; ln p t - 400 300 = t 2 &#8658; p t - 400 = 300 e t 2 &#8658; 400 - p t = 300 e t 2 &#160;&#160;&#160;( &#8756; p t &#60; 400 ) &#8658; p t = 400 - 300 e t 2

Let the population of rabbits surviving at a time t be governed by the differential equation d p t d t = 1 2…

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