2. (30 points) Antibiotic Treatment. A colony of bacteria is treated with a mild antibiotic agent so that the bacteria start to die. It is observed that the bacteria density decreases at a rate proportional to the density of bacteria present. Suppose the initial density of the bacteria is 100 cells per mL and let B (t) be the density of the bacteria at time t. (a) Write down an initial value problem that governs the density of the bacteria. [i.e., write down a rate equation and an initial condition). (b) It is noted when the density of the bacteria is 100 cells per mL, the density of the bacteria cells one hour later decreases by 25 cells per mL. Using your IVP and the given information, determine an equation that predicts the density of the bacteria t hours later. [If you are unable to complete this part, use B(t) = SOs0'5t for part (c)). (c) How long does it take for a 99% of the bacteria to die