As dPdt=k1P−k2P=(k1−k2)P\frac{dP}{dt}=k_1P-k_2P=(k_1-k_2)PdtdP=k1P−k2P=(k1−k2)P then dPP=(k1−k2)dt\frac{dP}{P}=(k_1-k_2)dtPdP=(k1−k2)dt hence P=P0e(k1−k2)tP=P_0e^{(k_1-k_2)t}P=P0e(k1−k2)t where P0=P(0)P_0=P(0)P0=P(0)
2.if k1>k2k_1>k_2k1>k2 then as t→∞t\to\inftyt→∞ , P→∞P\to\inftyP→∞ (C)
3.if k1=k2k_1=k_2k1=k2 then P=P0P=P_0P=P0 for every ttt (E)
4.if k1<k2k_1<k_2k1<k2 then t→∞t\to\inftyt→∞ , P→0P\to 0P→0 (B)
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