EXERCISE 10.8

EXERCISE . . The rate of increase in the number of bacteria in a certain bacteria culture is proportional to the number present. Given that the number triples in hours, find how many bacteria will be present after hours? . Find the population of a city at any time t , given that the rate of increase of population is proportional to the population at that instant and that in a period of years the population increased from , , to , , . . The equation of electromotive force for an electric circuit containing resistance and self- inductance is E Ri L di dt , where E is the electromotive force is given to the circuit, R the resistance and L , the coefficient of induction. Find the current i at time t when E = . . The engine of a motor boat moving at m s / is shut off. Given that the retardation at any subsequent time (after shutting off the engine) equal to the velocity at that time. Find the velocity after seconds of switching off the engine. . Suppose a person deposits ` , in a bank account at the rate of % per annum compounded continuously. How much money will be in his bank account months later? . Assume that the rate at which radioactive nuclei decay is proportional to the number of such nuclei that are present in a given sample. In a certain sample % of the original number of radioactive nuclei have undergone disintegration in a period of years. What percentage of the original radioactive nuclei will remain after years? . Water at temperature  C cools in minutes to  C in a room temperature of  C . Find (i) The temperature of water after minutes (ii) The time when the temperature is  C ; log = −     . At . A.M. a woman took a cup of hot instant coffee from her microwave oven and