Differential Equations
Differential Equation
nta_abhyas_2025
Grade 12
Question:
The population $p(t)$ at a time $t$ of a certain mouse species satisfies the differential equation $\frac{dp}{dt} = 0.5p(t) - 450$. If $p(0) = 850$, then the time at which the population becomes zero is
Step-by-Step Solution
Key Concept: Apply appropriate integration techniques and boundary conditions to solve the differential equation
This is an integer-type question where the numerical answer is $2\ln 18$. The solution involves solving a differential equation with specific boundary conditions and evaluating the result at a particular point to obtain this logarithmic value.
Correct Answer: 2 ln 18