WBJEE · Maths · Differential Equations
The population \(p(t)\) at time \(t\) of a certain mouse species follows the differential equation \(\frac{d p(t)}{d t}=0.5 p(t)-450\). If \(p(0)=850\), then the time at which the population becomes zero is
- A \(\log 9\)
- B \(\frac{1}{2} \log 18\)
- C \(\log 18\)
- D \(2 \log 18\)
Answer & Solution
Correct Answer
(D) \(2 \log 18\)
Step-by-step Solution
Detailed explanation
\(\frac{d p}{d t}=0.5 P-450\) or, \(\int_{850}^0 \frac{d p}{P-900}=\int_0^{\mathrm{t}} \frac{\mathrm{dt}}{2}\) or, \([\ln |\mathrm{P}-900|]_{850}^0=\frac{\mathrm{t}}{2}\) or, \(\frac{t}{2}=\ln \left|\frac{900}{50}\right|=\ln |18|\) or, \(t=2 \ln |18|\)
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