\(\frac { dy }{ dx } +\frac { y }{ x } =0,\) where 'x' denotes the percentage population in a city and 'y' denotes the area for living healthy life of population. Find the particular solution when \(x=100,y=1.\) Is higher density of population harmful? Justify your answer

Suppose the growth of a population is proportional to the number present. If the population of a colony doubles in 50 months, in how many months will the population becomes triple?

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

In a culture,the bacteria count is 1,00,000. The number is increased by 10% in 2 hours. In how many hours will the count reach 2,00,000, if the rate of growth of bacteria proportional to the number present?

The rate of increases in the number of bacteria in a certain culture is proportional to the number present. Given that the number triples in 5 hours, find how many bacteria will be present after 10 hours. Also, find the time necessary of bacteria to be 10 times the number initially present.\(\left( { log }_{ e }3=1.0986,{ e }^{ 2.1972 }=9 \right) \)  (approx.)