The population $p$ of the city at time $t$ is given by $\frac{dp}{dt} = \frac{p}{2} - 100$. If the initial population at $t = 0$ is $100$,then $p$ is:

The orthogonal trajectories of the family of curves $x^{2/3} + y^{2/3} = a^{2/3}$,where $a$ is an arbitrary constant,are given by:

The decay rate of radium is proportional to the amount present at any time $t$. If initially $60 \text{ gms}$ was present and half-life period of radium is $1600 \text{ years}$, then the amount of radium present after $3200 \text{ years}$ is (in $\text{ grams}$)

If a body is heated to $110^{\circ} C$ and placed in air at $10^{\circ} C$,and after $1 \text{ hour}$ its temperature is $60^{\circ} C$,then the additional time required for it to cool to $30^{\circ} C$ is

The decay rate of radioactive material at any time $t$ is proportional to its mass at that time. The mass is $27 \text{ grams}$ when $t=0$. After $3 \text{ hours}$,it was found that $8 \text{ grams}$ are left. Then the substance left after one more hour is

The solution of the differential equation $\frac{dy}{dx} = \frac{a + bx}{c + dy}$ represents a family of circles centered at the origin if...