In: Math
1. A tank starts with 100 litres of water and 1,000 bacteria in it. For now we assume the bacteria do not reproduce. Let B(t) be the number of bacteria in the tank as a function of time, where t is in hours. For each of the situations below, write down a first order differential equation satisfied by B(t), of the form dB dt = f(t, B). You DO NOT need to solve it.
(a) A little goblin is pouring bacteria into the tank at a rate of 2020 bacteria per hour.
(b) Like part (a), but we are also draining the tank at a rate of 3 litres per hour.
(c) Like part (b), but now the bacteria are reproducing. Suppose that the bacteria will double the present population in every hour. A gentle reminder: make sure that you write down the meaning of each term.