The population P = P(t) at time 't' of a certain species follows the differential equation
${{dP} \over {dt}}$
= 0.5P – 450. If P(0) = 850, then the time at which population becomes zero is :
Solution
${{dp} \over {dt}} = {{p - 900} \over 2}$<br><br>$\int\limits_{850}^0 {{{dp} \over {p - 900}} = \int\limits_0^t {{{dt} \over 2}} }$<br><br>$\Rightarrow$ $\ln |p - 900|_{850}^0 = {t \over 2}$<br><br>$\Rightarrow$ $\ln 900 - \ln 50 = {t \over 2}$<br><br>$\Rightarrow$ ${t \over 2} = \ln 18$<br><br>$\Rightarrow t = 2\ln 18$
About this question
Subject: Mathematics · Chapter: Differential Equations · Topic: Order and Degree
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