A) \[\frac{\alpha }{\lambda }\left( 1-{{e}^{-\lambda t}} \right)\]
B) \[\alpha -\frac{\alpha }{\lambda }{{e}^{-\lambda t}}\]
C) \[\frac{\alpha }{\lambda }{{e}^{-\lambda t}}\]
D) \[\alpha \left( 1-{{e}^{-\lambda t}} \right)\]
Correct Answer: A
Solution :
[a] \[\frac{dN}{dt}=\alpha -\lambda N\] \[\int_{0}^{N}{\frac{dN}{\alpha -\lambda N}}\,\,\,=\int_{0}^{t}{dt}\] Solving \[N=\frac{\alpha }{\lambda }\,\,(1-{{e}^{-\lambda t}}).\]
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