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

The family of curves whose $x$ and $y$ intercepts of a tangent at any point are respectively double the $x$ and $y$ coordinates of that point is

The population of a village increases at a rate proportional to the population at that time. In a period of $10$ years,the population grew from $20,000$ to $40,000$. Then,the population after another $20$ years is:

The equation of a curve passing through $\left( 2, \frac{7}{2} \right)$ and having gradient $1 - \frac{1}{x^2}$ at $(x, y)$ is:

The population of a village increases continuously at a rate proportional to the number of its inhabitants present at any time. If the population of the village was $20,000$ in $1999$ and $25,000$ in the year $2004,$ what will be the population of the village in $2009?$

The differential equation $\frac{dy}{dx} = \frac{\sqrt{1-y^2}}{y}$ determines a family of circles with