JEE Mains · Maths · STD 12 - 9. differential equations
The population \(P = P ( t )\) at time \({ }^{\prime} t ^{\prime}\) of a certain species follows the differential equation \(\frac{ dP }{ dt }=0.5 P -450 .\) If \(P (0)=850,\) then the time at which population becomes zero is
- A \(\log _{ e } 18\)
- B \(\log _{ e } 9\)
- C \(\frac{1}{2} \log _{ e } 18\)
- D \(2 \log _{ e } 18\)
Answer & Solution
Correct Answer
(D) \(2 \log _{ e } 18\)
Step-by-step Solution
Detailed explanation
\(\frac{ dP }{ dt }=0.5 P -450\) \(\Rightarrow \quad \int_{0}^{ t } \frac{ dp }{ P -900}=\int_{0}^{ t } \frac{ dt }{2}\) \(\Rightarrow \quad[\ell n | P ( t )-900|]_{0}^{ t }=\left[\frac{ t }{2}\right]_{0}^{ t }\)…
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