A population P(t) of field mice, where P is the number of mice and t is measured in months from some starting point, grows at the rate of 50% per month. However, owls in the neighbourhood eat them at the rate of 600/month. A model for the mice population is given by the differential equation dP —D 0.5Р — 600 dt If the field can only sustain a capacity population of k = 10000 field mice, can you state a better model for the mice population in which populations do not grow to infinity?

Given that a population $P\left(t\right)$ of field mice, where $P$ is the number of mice and $t$ is the measured in months from starting point at the rate of 50% per month. So, the growth rate is 

$r=0.5$

Owls in the neighborhood eat them at the rate of 600 per month which is constant.

The field can only sustain a capacity population of $\kappa =10,000$. therefore, maximum carrying capacity is $\kappa =10,000$.

Since, there is a maximum carrying capacity, it restricts the growth due to lack of available resources or other reason. In that case, population do not grow to infinity.