A culture of bacteria doubles every 5 hours. After 15 hours, the sample contains 144 000 bacteria. Write a function to model the bacteria population over time in hours. Define each of your variables properly. Justify why you think this scenario cannot be modelled by the other function. Demonstrate how you logically obtain the values of the parametres to receive full marks. A Determine the derivative function. Show all your steps, including descriptors of what derivative rules are used in the process Plot the derivative function on the same graph as the original function using Desmos. Use different colours to distinguish between your original and derivative functions. Then place the screenshot of your graph on your PowerPoint slide. c) How fast are the bacteria growing at the 24th hour?