Answer PART C to year 11 standard of Calculus

2= V AL AaBbCcDdE AaBbCcDdE Aa BbCcDc AaBl A E Normal No Spacing Heading 1 He Stage 1 Mathematical Methods Modelling Bacterial Growth Task: Bacteria are everywhere! Environmental factors can impact on bacterial growth rates. In this investigation, you will use calculus to model bacterial populations and discuss the impact of common disinfectants and surfaces on their growth. Part A The population p, in thousands of bacterial colonies on a kitchen bench can be modelled by the function p(t) = 200 + 20t - t? where t is time in hours. a) State the initial population. b) Determine the growth rate of the population in terms of t c) What does it mean when p' (t) = 0? Calculate the value of t when this occurs and explain what this answer means. d) Explain what happens to p'(t) for t greater than the value you found in part c. Give one reason why this might occur. Part B The growth of a similar population was investigated after spraying a kitchen bench 300 Population (P) with Glen 20 disinfectant. The blue parabola represents the new model and the red (1.5, 202.25) parabola is the population from Part A. 200 a) Use calculus methods to find the equation g(t) for the new model b) Construct a graph of p'(t) and g'(t). c) State the time interval for which g'(t) is increasing. d) Compare the population growth rate for the two models when t = 1, t = 5 -20 20 and t = 10. Explain what is happening time () to each population. Part C Some scientific papers state that the presence of silver nanoparticles on a surface can inhibit bacterial population growth by 90%. Other papers state that the bacterial population growth can be inhibited by 50%. Use your methods from Parts A and B to model and compare the two findings. Identify reasons as to why these scientists may have gotten different results. X Accessibility: Investigate