1. A tank starts with 100 litres of water and 1,000 bacteria init. For now we assume the bacteria do not reproduce. Let B(t) bethe number of bacteria in the tank as a function of time, where tis in hours. For each of the situations below, write down a firstorder 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 rateof 2020 bacteria per hour.
(b) Like part (a), but we are also draining the tank at a rateof 3 litres per hour.
(c) Like part (b), but now the bacteria are reproducing. Supposethat the bacteria will double the present population in every hour.A gentle reminder: make sure that you write down the meaning ofeach term.
