Question

The population \( p(t) \) at time \( t \) of a certain mouse species satisfies the differential equation:
\[ \frac{d p(t)}{dt} = 0.5p(t) - 450. \] If \( p(0) = 850 \), then the time at which the population becomes zero is:

• A. \( 2 \ln 18 \)
• B. \( \ln 9 \)
• C. \( \frac{1}{2} \ln 18 \)
• D. \( \ln 18 \)

Hint:

For solving first-order linear differential equations, use separation of variables and then integrate to find the general solution.