Math/Physic/Economic/Statistic Problems
Write a program in Python to calculate the surface area of a cuboid. Collect width, height and depth of the cuboid as input.
(2 mark)
Write a program that will work out the distance travelled if the user enters in the speed and the time.
(2 mark)
Write a program to calculate the area of a circle from the radius entered by the user.
(2 mark)
Write a program to calculate the future value (FV) of a loan using compound interest.
(3 mark)
𝐹𝑉 = 𝑃𝑉(1 + 𝑟)𝒏
PV = present value
r = interest rate (as a decimal value) n = number of periods
In your own words, provide a definition of Mathematical modelling and explain three components which contributes to a good mathematical model. Think of one or more real-world scenario in which mathematical modelling can be used to provide insights, solutions, and predictions.
(2 marks)
Explain the importance of assumptions in building a mathematical model. Use one or two examples to further clarify your answers.
(2 marks)
Explain three possible limitations of using mathematical model as a data scientist. Use some real-world example(s) to illustrate your answers.
(3 marks)
Suppose that one of your hobbies is to collect ants and put them in a jar. One day after coming to mathematical modelling seminar, you are interested in modelling the growth of your ant’s colony population.
Explain using the 1st stage of mathematical modelling how you would define the objective of your model, the assumptions regarding your ants’ population, the level of simplifications, and your model function or formula. (hint: suppose P = population and t=time (day), what is the function for your ants population growth in terms of time ) (3 marks)
What technique of mathematics is used to model the scenario above? Suggest some ways for you to validate your model in (i) (2 mark)
