jee-main 2014 Q86

jee-main · India · 06apr Differential equations Applied Modeling with Differential Equations

Let the population of rabbits surviving at a time $t$ be governed by the differential equation $\frac { d p ( t ) } { d t } = \frac { 1 } { 2 } \{ p ( t ) - 400 \}$. If $p ( 0 ) = 100$, then $p ( t )$ equals
(1) $600 - 500 e ^ { \frac { t } { 2 } }$
(2) $400 - 300 e ^ { \frac { - t } { 2 } }$
(3) $400 - 300 e ^ { t / 2 }$
(4) $300 - 200 e ^ { \frac { - t } { 2 } }$

Let the population of rabbits surviving at a time $t$ be governed by the differential equation $\frac { d p ( t ) } { d t } = \frac { 1 } { 2 } \{ p ( t ) - 400 \}$. If $p ( 0 ) = 100$, then $p ( t )$ equals\\
(1) $600 - 500 e ^ { \frac { t } { 2 } }$\\
(2) $400 - 300 e ^ { \frac { - t } { 2 } }$\\
(3) $400 - 300 e ^ { t / 2 }$\\
(4) $300 - 200 e ^ { \frac { - t } { 2 } }$

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