I got a question on a math quest book.
The questions said in a lake, the population of bacteria will grow at a rate that is proportional to their current population and that in the absence of any outside factors the population will double every 10 days. It is estimates that, on average, (it is an outside factor), on any given day 8% of them will die. The current population is 100.
Will this population survive or die out eventually?
How could I use differential to model this problem?
If I let P(t) be the population changes with time t (in days),
I know that without outside factor, P(t) = 100*2(t/10)
and with that outside factor, P(t) = P(t-1)*0.92
and P(0) = 100.
Then is it true to say that dP/dt = P*2(t/10) ?
Or how could I set up the equation of dP/dt ?
Hope you could give me some inspiration.