The population p(t) at time t of a certain mouse species satisfies the differential equation dp(t)/dt = 0.5p(t). If p(0) = 850, then the time at which the population becomes zero is:

The given differential equation is dp(t)/dt = 0.5p(t).
This is a separable differential equation. We can rewrite it as:
dp(t)/p(t) = 0.5dt
Integrating both sides, we get:
∫dp(t)/p(t) = ∫0.5dt
ln|p(t)| = 0.5t + C
where C is the constant of integration.
Since p(t) represents population, it must be positive. Therefore, we can remove the absolute value sign:
ln(p(t)) = 0.5t + C
p(t) = e^(0.5t + C) = e^(0.5t) * e^C
Let A = e^C, then p(t) = Ae^(0.5t).
Using the initial condition p(0) = 850, we have:
850 = Ae^(0.5*0) = A
So, p(t) = 850e^(0.5t).
The population becomes zero when p(t) = 0. However, the exponential function e^(0.5t) is always positive, so p(t) will never be exactly zero. The population will approach zero as t approaches negative infinity. There is no time at which the population becomes exactly zero. The question is flawed in posing this as a possible solution.