Question

The population of bacteria in a culture is increasing and the rate of increase is proportional to the number of bacteria present in the culture. If initially the culture contains 50 bacteria and at the end of 2 hours there are 500 bacteria in the culture, how many bacteria will be present at the end of 5 hours?

Answer 1

If we determine the constant P0 and k, we will have found the precise form of the function P(t) exactly. It is given that there are 50 bacteria initially so we take t=0 as the initial time, then

is obtained. Since there are 500 bacteria in this culture at the end of 2 hours, one can obtain

If we take ln both of sides of the equation 10 = e^k.2,

is obtained. As a result, the function that gives the number of the bacteria present at time t is  Now we can calculate the number of bacteria after 5 hours in the culture as