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.

Express each of the following physical statements in the form of differential equation. (ii) The population P of a city increases at a rate proportional to the product of population and to the difference between 5,00,000 and the population.

Express each of the following physical statements in the form of differential equation. (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.

Express each of the following physical statements in the form of differential equation. (iv) A saving amount pays 8% interest per year, compounded continuously. In addition, the income from another investment is credited to the amount continuoulsy at the rate of Rs. 400 per year.

Express each of the following decimals in the p/q form 2.104

Express each of the following decimals in the p/q form 0.35

Express each of the following decimals in the p/q form -8.005

Express each of the following decimals in the (p)/(q) form 0.75

Express each of the following decimal in the p/q form 1.00001