Surge function in modelling medicinal doses

the requirements and what we going to do are all in below(that file). I want someone can help me to write this. I want get at lease B

Stage 2 Mathematical Methods Assessment Type 2: Mathematical Investigation Surge and Logistic Models The Surge Function A surge function is in the form 𝑓(𝑥) = 𝐴𝑥𝑒 −𝑏𝑥 where A and b are positive constants. • On the same axes, graph 𝑦 = 𝑓(𝑥) and 𝑦 = 𝑓’(𝑥) for the case where 𝑨 = 𝟏𝟎 and 𝒃 = 𝟒 𝑖. 𝑒. 𝑓(𝑥) = 10𝑥𝑒 −4𝑥 • • • • • • • • Determine the coordinates of the stationary point and point of inflection and label these on the graph. Repeat the investigation for three different values of 𝑨 while maintaining 𝒃 = 𝟒. Include your graphs in the report and summarise the findings in a suitable table. State the effect of changing the value of 𝑨 on the graph of 𝑦 = 𝐴𝑥𝑒 −𝑏𝑥 . Using a similar process investigate the effect of changing the value of 𝒃 on the graph of 𝑦 = 𝐴𝑥𝑒 −𝑏𝑥 . Make a conjecture on how the value of b effects the x-coordinates of the stationary point and the point of inflection of the graph of 𝑦 = 𝐴𝑥𝑒 −𝑏𝑥 . Prove your conjecture. Comment on the suitability of the surge function in modelling medicinal doses by relating the features of the graph to the effect that a medicinal dose has on the body. Discuss any limitations of the model. At least four key points should be made. The Logistic Function 𝐿 A logistic function is in the form 𝑃(𝑡) = 1+𝐴𝑒 −𝑏𝑡 where 𝑳, 𝑨 and 𝒃 are constants and the independent variable t is usually time; 𝑡 ≥ 0. This model is useful in limited growth problems, that is, when the growth cannot go beyond a particular value for some reason. • Investigate the effect that the values of 𝐿, 𝐴 and 𝑏 have on the graph of the logistics function. • Discuss your findings on the logistic model. • Relate the specific features of the logistic graph to a limited growth model. At least three key points should be made. Modelling using Surge and Logistic Functions Using either a surge or a logistic function (or both) develop a model to investigate one of the following scenarios. • • • • • • • • • Movements of students into the school building at the end of lunch. A crowd leaving a sports venue. The limited growth of a population. pH levels in a titration. Repeat doses of a medicine. The spread of information in a group of people. Traffic density during peak hour.