The population p(t) at time t of a certain mouse species satisfies the differential equation dp(t)/dt = 0.5 p(t) - 450 . If p(0) = 850 , then the time - Mathematics MCQ AIEEE 2012 2026 | ExamTest.live

mediumMCQAIEEE 20122026Mathematics

1 mark

The population p (t) at time t of a certain mouse species satisfies 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:

Solution & Step-by-step Explanation

\frac{d p}{d t} = 0.5 p - 450 = \frac{p - 900}{2} Separating variables: \frac{d p}{p - 900} = \frac{1}{2} d t Integrating both sides: ln ∣ p - 900∣ = \frac{t}{2} + C Given p (0) = 850 : ln ∣850 - 900∣ = 0 + C ⟹ C = ln 50 So, ln ∣ p - 900∣ = \frac{t}{2} + ln 50 To find t when p (t) = 0 : ln ∣0 - 900∣ = \frac{t}{2} + ln 50 ln 900 = \frac{t}{2} + ln 50 \frac{t}{2} = ln 900 - ln 50 = ln (\frac{900}{50}) = ln 18 t = 2 ln 18

Try it yourself before checking the explanation above.

The population p (t) at time t of a certain mouse species satisfies 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:

2 ln 18

ln 9

\frac{1}{2} ln 18

ln 18

Practice with timed mock tests and track your performance across Mathematics.