Student Name:
MHF4U/ Final Project part 2
MHF4U
Final Project
Part 2
Requirements:
Make sure to read and follow the instructions carefully
Complete all the requirement and hand in the necessary documents
Students need to bring graphing calculatoror laptop which is equipped with technology software to class in order to finish task in class.
Evaluation:
The full mark for this part is 65.
Instructions:
The final project will be given by the teacher in-class.
After finishing this project, each student need to hand-in a formal answer sheet. Since most of the questions need to be solved by using Graphing Technology, therefore, when you use the graphing technology to solve the questions, please Screenshot and print your procedures and enclose it with your answer sheet.
During this project, your teacher may ask yousome questions related to what you do. If you fail to answer the questions, you may lose marks.
This project is individual project. Therefore, the students are required to complete this project independently. No plagiarism or cheating is tolerated.
Students are allowed to use in-class or online materials to solve the question effectively.
Notice the teacher will evaluate based on success criteria for each student. Therefore, please show the whole detail solving problem procedure as well as demonstrate how you connect the course knowledge to applied questions in your answer sheet.
This part is 65 marks.
Part II: This part include two tasks, students have to finish these tasks in computer lab and hand in an answer sheet
Task IV: Global Population Growth (D2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 3.1, 3.2, 3.3)
The global population has grown from 1 billion in 1800 to 7 billion in 2012. It is expected to keep growing. Estimations have put the total population at 8.4 billion by mid-2030, and 9.6 billion by mid-2050. Many nations with rapid population growth have low standards of living, whereas many nations with low rates of population growth have high standards of living.1
The following data gives the population over a period of 23 years in a developing country.
Use Graphing Calculator to create a scatter plot of the data and determine a mathematical function model that represents this data. (Hint: it is a cubic function).
1. "2013 World Population Factsheet" . www.pbr.org. Population Reference Bureau. Retrieved 2 November 2017
Questions:
Determine using Graphing Calculator or Fathom, the domain, range, maximum/ minimum points of the combining function d (t), which equal to the sum of the equations above (k,t). Explain what kind of factors will affect these properties? (k,t,c)(D2.1)(5points)
Write the equation of the function that models this situation, with the necessary parameters (k,t). Graph the function you determine using Graphing Calculator or Spreadsheet (k). Use the graph to determine the population rate of change of the whole time interval (k,t,a). Check that it models the growth of population correctly (k,t). (D2.2, 2.4 half, 2.6)(5points)
Determine when the population growth reaches a minimum and what the minimum population growth is (k,t). Determine how long will it takes for this country to reach the population of 1 billion (k,t). Compare your results and verifying using Graphing Calculator(k,t).(D3.3)(3points)
General question :
a) Let and , determine the function y = ( f *g)(x).(k,t)(2points)
b) Determine the expression y = (f ° g)(x). And then sketch the graph of the composition function using Graphing Calculator(k,t).Explain the meaning of this composition of function for this problem.(k,t,c)(D2.4 half)(2points)
Whether the products of two functions (f(x) + g(x); f(x)g(x)) are odd or even if the two functions are both even or both odd, or if one function is odd and the other is even. Investigate algebraically, and verify numerically and using Spreadsheet.(k,t,c)(D2.3)(6points)
Given , Verify that f -1(f(x))=f ( f -1(x)) algebraically and graphically by sketching both original and inverse function and comparing their properties(D2.7) (5points)
(K(U), T, A)In the following case, function f and g are defined for x ∈ R. Determine the expression, domain and range of f(g(x)) and g( f(x)). Verify that f( g(x) is not always equal to g( f(x)).(k,t)(D2.5)(5points)
f(x) = 2x2 + 3x + 6, g(x) = 4x + 3
f(x) = 4 and g(x) =5x. State the values of for which f(x) < g(x), f(x) = g(x), and f(x) > g(x).(k,c) Express the values to the nearest tenth (k,c). Verify your answers using Graphing Calculator. (k,t)(D3.2)(2points)
Compare using Graphing Calculator or Spreadsheet the graph f(x) = 2x2+5 with the graph of f(g(x)) and g( f(x)), where g(x) =2(x – d), for various values of d(k,t). Describe the effects of d in terms of transformations of f(x)(k,c). (D2.8)(6points)
Copy the following table, and complete by inspecting the algebraic representation of the functions (k,t). Compare the features by using Graphing Calculator or Fathom(k,t). Explain how the equation forms affect the features (k,c). (D3.1)(3points)
Task IV: Decay of Plutonium(A1.1, 1.2, 1.3, 1.4, 2.1, 2.2, 2.3, 2.4, 3.1. 3.2, 3.3, 3.4)
In an experiment, the mass of Plutonium-238 decayed every hour. The results are given in the following table.
Questions:
Graph the data for this experiment and determine the equation that bet models the data (k). (Hint: it is an exponential function). Determine and graph the corresponding logarithmic function and describe the relationship between the exponential function and logarithmic function based on their graphs (k,t,c). Verify your findings using Graphing Calculator or Online Graphing Tool. (A2.2)(2points)
Make up your own question that could be solved using logarithmic and exponential functions (k,t,a). You can either interpolate or extrapolate your function (A2.4, 3.4)(2points)
General Questions:
Determine the approximate value of the following logarithm functions using graphing calculator: (A1.1 half, 1.2)(k)(2points)
a)
b)
Why is it not possible to determine or ? Explain your reasoning. (A1.1 half)(k,t,c)(2points)
Express in logarithmic form or exponential form. (A1.3)(k)(2points)
a)
b)
(K(U), A)Explain why + = 0, and verify using patterning (k,t,c). And then use the laws of logarithms to simplify and evaluate the following expression (k,t). (A1.4 half)(2points)
Determine an equivalent expression for). (A1.4 half) (k,t)(1points)
Solve =+. (k)(A3.3)(1points)
Using Graphing Calculator or Spreadsheet and without using technology to answer what does the graph of a logarithmic function look like and what are its characteristics (vertical and horizontal asymptotes, domain and range, increasing/ decreasing behaviour) (k,t,a)? Compare the results between your algebraic representation and graphical representation (k,t). (A2.1)(2points)
What transformations must be applied to to graph (k,t)? Identify the transformations that are related to the parameters a, k, d, and c in the general logarithmic function, and then verify your result using Graphing Calculator:(k,t)(A2.3)(2points)
Solve and either by finding a common base and by taking logarithms (k,t), and explain your choice of method in each case (k,t,c). And then solving by taking the logarithm base 10 of both sides (k). (A3.2)(2points)
Sketch the graphs of and, compare the graphs, and explain your findings algebraically. (k,t,a)(A3.1)(1points)