Hmm... nice one!
I'll give it a try, although you should look for a second opinion, ok?
With denote the number of bacteria in the begining,
Rate of increase in bacteria population clearly depends on the number of bacteria: greater the number of bacteria, greater the increase in their number. This statement has nothing to do with mathematics, its pure common sense, but it is crucial information to have if one wants to solve the problem. Instead of increase lets use the term rate of growth (of the whole culture), representing the change in the number of bacteria in time, and denote it with
Then denoting the number of bacteria in a certain moment in time can be calculated from the equation: Number to begin with plus rate of growth in time multiplied by time elapsed from the beginning.
Now put to use the information given to you:
Sentence "the number of bacteria increased sixfold in 10 h" translates to the following equation: . This equation enables us to come up with the rate of growth: . I mentioned that the rate of growth of bacteria depends on their number and this is the proof of that.
Now we have the formula for calculating the number of bacteria: . Time needed for the number of bacteria to double can be translated to equation: find the value of variable such that
So, you have: . Divide by (you can do that since because you had to have some bacteria to begin with in the first place). Now it follows:
so it would take 2 hours for the culture to double its numbers.