A) \[2\,\ell n18\]
B) \[\ell n\,9\]
C) \[\frac{1}{2}\ell n\,18\]
D) \[\ell n\,18\]
Correct Answer: A
Solution :
\[2\frac{dp(t)}{900-p(t)}=-dt\] \[-2\ell n(900-p(t))=-t+c\] when \[t=0,p(0)=850\] \[-2\ell n(50)=c\] \[\therefore \] \[2\ell n\left( \frac{50}{900-p(t)} \right)=-t\] \[900-p(t)=50\,\,{{e}^{t/2}}\] \[p(t)=900-50\,\,{{e}^{t/2}}\] let \[p({{t}_{1}})=0\] \[0=900-50\,\,{{e}^{\frac{{{t}_{1}}}{2}}}\] \[\therefore \] \[{{t}_{1}}=2\ell n\,\,18\]
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