take time as measured in hours.Bacteria in a culture increase at a rate proportional to the number present. An initial population of 200 triples in 10 hours. If this pattern of increase continues unabated, then the approximate number of bacteria after 1 full day is?

You are told that the population satisfies the differential equation:

for some constant .

hence:

Put and we get:

Also we have:

so:

Now evaluate .

CB