It given that the rate at which some bacteria multiply is proportional to the instantaneous number presents. If the original number of bacteria doubles in two hours, in how many hours will it be five times?

The rate of increase in the number of bacteria in a certain bacteria culture is proportional to the number present. Given the number triples in 5 hrs., find how many bacteria will be present after 10 hours. Also find the time necessary for the number of bacteria to be 10 times the number of initial present. [Given log_e3=1. 0986 ,\ e^(2. 1972)=9 ]

In a certain culture the number of bacteria at any instant increases at a rate proportional to the cube root of the number present at that instant. If the number becomes 8 times in 3 hours, when will the number be 64 times?

The rate of increase of the bacteria in a culture is proportional to the number of bacteria present and it is found that the number doubles in 6 hours. Prove that the bacteria becomes 8 times at the end of 18 hours.

The amount of time it takes to consume a buffalo carcass is inversely proportional to the number of vultures. IF it takes 12 vultures 3 day to consume a buffalo, how many fewer hours will it take there are 4 more vultures?

The amount of time tha Amy walks is directly proportional to the distance that she walks. If she walks a distance of 2.5 miles in 50 minutes, how many miles will she walk in 2 hours?

The rate of growth of a population is proportional to the number present. if the population of a city doubled in the past 25 years, and the present population is 100000, when will the city have a population of 500000? [Given, log_e 5 = 1.609 , log_e 2 = 0.6931 . ]

The amount of time it take to consume a buffalo carcasess is inversly proporation to the number of vultures. If it takes 12 vultures 3 days to consume a buffalo, how many fewer hours will it take if there are 4 more vultures?

A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there is 50 kg of the material present and after two hours it is observed that the material has lost 10% of its original mass, find () and expression for the mass of the material remaining at any time t, (ii) the mass of the material after four hours and (iii) the time at which the material has decayed to one half of its initial mass.

A certain radioactive material is known to decay at a rate proportional to the amount present. If initially there is 50 kg of the material present and after two hours it is observed that the material has lost 10% of its original mass, find () and expression for the mass of the material remaining at any time t, (ii) the mass of the material after four hours and (iii) the time at which the material has decayed to one half of its initial mass.

The rate at which radioactive substances decay is known to be proportional to the number of such nuclei that are present in a given sample. In a certain sample 10% of the original number of radioactive nuclei have undergone disintegration in a period of 100 years. Find what percentage of the original radioactive nuclei will remain after 1000 years.