3) [10 marks| Suppose a new mutant bacteria is able to double every 15 minutes. You are infected with 1 of these mutant bacteria. a) How many bacterial are there in 1 hour? By what factor did the number of bacteria increase in one hour? b) What is the general solution (model) that describes the bacteria population size at time 'n', in hours? c) Use your answer to part b) to determine the number of bacteria in 4 hours. d) At what time, in hours, will there be at least 16M bacteria? You may use online tools to answer this question. If you use an online tool, you must describe (screenshot etc.) the steps taken. Approximate answers are fine. e) Write out a recursive equation for this problem. Your time interval should be in hours. Confirm your recursion is correct by using it to solve for the number of bacteria in 2 hours. 4. [2 marks] Using the steps outlined in class, draw a nautilus shell. Make sure that the spiral is counter- clockwise. Note: this can be a sketch and does not need to be perfectly to scale