EXERCISE . . Express each of the following physical statements in the form of differential equation. (i) Radium decays at a rate proportional to the amount Q present.
(ii) The population P of a city increases at a rate proportional to the product of population and to the difference between , , and the population. (iii) For a certain substance, the rate of change of vapor pressure P with respect to temperature T is proportional to the vapor pressure and inversely proportional to the square of the temperature. - - (iv) A saving amount pays % interest per year, compounded continuously. In addition, the income from another investment is credited to the amount continuously at the rate of ` per year.
. Assume that a spherical rain drop evaporates at a rate proportional to its surface area. Form a differential equation involving the rate of change of the radius of the rain drop.