A) \[400-300\,{{\text{e}}^{\text{t/2}}}\]
B) \[300-200\,{{\text{e}}^{\text{-t/2}}}\]
C) \[600-500\,{{\text{e}}^{\text{t/2}}}\]
D) \[400-300\,{{\text{e}}^{\text{-t/2}}}\]
Correct Answer: A
Solution :
Rearranging the equation we get, \[\frac{dp(t)}{p(t)-400}=\frac{1}{2}dt\] ?(1) Integrating (1) on both sides we get\[p(t)=400+k{{e}^{t/2}},\]where k is a constant of integration. Using p(0) = 100, we get k = −300 \[\therefore \]the relation is\[p(t)=400-300\text{ }{{e}^{t/2}}\]
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