Complete a mathematical modelling project and report based on the following brief: The populations of humans and other organisms change over time. The population of a community (e.g. village, town, county, country, planet) will change due to rates of births and deaths, but it will also change due to migration. Changes in populations may be influenced by factors such as economic development, famine, drought, disease, war, technological improvements, etc. Based on historical data, mathematical models may be developed to predict the sizes of future populations. Mathematical models of populations may be developed to include some or all of: ⚫ linear functions • • polynomial functions of degree n logarithmic/exponential functions recurrence relations difference equations (nth order homogeneous or inhomogeneous, n Є N) • differential equations ⚫ combinations of the above ⚫ other functions, equations and mathematical models Select one or more aspects of population change for humans or other organisms. Model the problem(s) you have selected using the cycle described in The Modelling Cycle section of this document. Acknowledgements Images parisschoolofeconomics.eu irishexaminer.com newstalk.com population.un.org/wpp emn.ie Geataí Imeachta Departure Gates Eitilti Isteach Arrivals Leaving Certificate Examination Applied Mathematics - Higher and Ordinary Level Mathematical Modelling Project - 2025 6

Q: Consider a simplified version of American football where on any possession ateam can earn 0, 3 or 7…

A: x (7s)y (3s)Total Points00 to 40, 3, 6, 9, 1210 to 37, 10, 13, 1620 to 214, 17, 2030 to 121, 244028

Q: In the context of Linear Algebra, how would this be solved?

A:

Q: Can you help me answer question 12 and question 14 (all use numerical method )numet subject

A: QUESTION 12: Predicting Power Output Based on Speed and Torque Data Table:x₁: Speed (rpm)x₂: Torque…

Q: Pls help on all asked.

A: Given:Mean (μ) = 215 hoursStandard Deviation (σ) = 12 hoursThe lifetime of the bulbs is normally…

Q: please ignore the work already done for these as i am not sure they are correct.

A: Solution to exercise 5(2c): Recursive definition of  ρ(n)=2n(n+1) The mapping  ρ:N→N is…

Q: Pls help ASAP

A:

Q: a) If is a polynomial function, does always have to have a horizontal asymptote? If no, provide a…

A: Step 1: Step 2: Step 3: Step 4:

Q: In 2007 the New York Times reported that the median annual household income in the United States was…

A: Statistical Analysis of 2013 Household Income Sample (n = 14)Raw Data (in $1,000s):49.4, 52.4, 53.4,…

Q: Find the convolution of the signals y[n], x[n]x[n]=(1-n)u[n+2]u[-(n-2)]y[n]=nu[n+1]u[1-n].

A: ____________________________________________________________________________________________________…

Q: Q1: solve the system y 2 In √√x² + y2 X y = −y + In √√x² + y2 and solve the linear part.

A: Step 1: Identify the Linear SystemThe given system is: x˙=−x−lnx2+y2​y​ y˙​=−y+lnx2+y2​x​To extract…

Q: Construct a know-show table of the proposition: For each integer n, n is even if and only if 4…

A: Proposition: For every integer  n,  n is even if and only if  4 divides  n2.  DirectionWhat We…

Q: iation 7. Let f be continuous on [a, b] and differentiable on (a, b). If lim f'(x) xia exists in R,…

A:

Q: (a) For the following linear programme, sketch the feasible region and the direction of the…

A: Step 1: Step 2: Step 3: Step 4: Step 5: • The feasible region is unbounded because there are no…

Q: Obtain the voltage across the capacitor for the following input: (a) 5Volts; (b) 3sin(t); (c) 2…

A: a: The capacitor charges exponentially towards 5 Volts with a time constant (τ=1sec).  b: The…

Q: 9) Write an equation for the hyperbola. 2+ -6-5-4-3-2 -2- -4- -5+ + 23 45 6x

A: It is required to write an equation for the given hyperbola. Identify the key features of the…

Q: This has to be done advanced mathematics report , also give the code for this. And do not give…

A:

Q: The manager of a fleet of automobiles is testing two brands of radial tires and assigns one tire of…

A:

Q: Recall the RSA encryption/decryption system. The following questions are based on RSA. Suppose n…

A: 1. Find an encryption key e for the pair (e, n)To find a valid encryption key e, we need to follow…

Q: provide step by step solution for the following questions. All computations must be done and shown…

A: SUMMARY. QuestionFinal AnswerQ1: WACC after debt10.9295%Q2: Shares to retain when…

Q: 5. The revenue function for a school group selling n cookies is given by R(n) = 2n, and the total…

A: Step 1:Problem 5: Cookies and Profit a) Determine a simplified equation for the profit function,…

Q: D D VVV Prove that it x=1 (mod 12), then x=4 (mod 3) and x=5(mod 4).

A:

Q: Find the volume of the parallelepiped with adjacent edges PQ, PR, PS. P(1,0, 2), Q(-5, 3, 7), R(3,…

A:

Q: Need detailed report solution without AI and Chatgpt,

A: May this answer helpful to you.

Q: Pls help ASAP

A:

Q: Pls help ASAP

A: 9. FalseThe profit function is given by P(n) = R(n) - C(n) (Revenue minus Cost). 10. f(g(-5))From…

Q: Pls help on all asked questions.

A: Let's define the variables: n: Number of T-shirts producedC(n) : Total cost functionR(n) : Revenue…

Q: Pls help ASAP

A: Step 1: Step 2:Step 3: Step 4:

Q: Pls help ASAP PLS ASAP

A: Step 1:Step 2:Step 3:Step 4:

Q: Q/prove that:- An edge only if e e of agraph G is abridge if and is not part of any cycle in G.

A: Step 1: Step 2:Step 3: Step 4:

Q: x²+8x+15 f(x) = Consider the function. x²-x-12 a) Determine the following key features of the…

A: Here's a more accurate graph sketch on Desmos for your reference.

Q: Q/ Solved by d'Alembert:- Utt = 5uxx u(x,o) - = sin X ut (X,0) = Sin 3X

A: Let's solve the given wave equation using d'Alembert's solution.Given:utt​=5uxx​Initial…

Q: 3. A construction worker is measuring wood to build a triangular side of a roof. The angle at the…

A: I hope you find this helpful.Thank you.

Q: Habitat for Humanity International is a nonprofit organization dedicated to eliminating poverty…

A:

Q: For all integers a and b if a is congruent to 0(mod n) and b is congruent to 0(mod n) then a+b is…

A: Here is a Know-Show Table to prove that:Statement:For all integers a and b, if:a ≡ 0(mod n)a and b ≡…

Q: 1. Given X' = X 3 e2t (a) Verify that X₁(t) = (e) and X2(t) = (et) - are solutions to the given…

A: a d)

Q: 3. Let Pk denote the vector space of all polynomials with degree less than or equal to k. Define a…

A: Step 1: Step 2: Step 3: Step 4:

Q: 3. Consider the matrix C = - (3) 2 0 2 0 0 Decide whether the matrix C is diagonalizable or not. If…

A:

Q: Pls help on all asked.

A: QuestionAnswer12C. 713B. $1.5014D. 0.0315C. mean = 3, standard deviation = 1.72

Q: 1. Locate the singularities of three of the following functions, and determine their type. (a)…

A: (a)  f(z)=z−1(z−sinz) Step 1: Simplify the function: f(z)=zz−sinz​ Step 2: Analyze singularities: We…

Q: Can you show me a step by step explanation please.

A:

Q: how to construct the following same table?

A: The Dirichlet character table modulo 21 lists the values of 12 distinct characters, each defined on…

Q: q5) instructions and question in images

A: We are given the differential equation:dxdy​=x2y+x3cosx​ Step 1: Rearranging the equationWe can…

Q: 1 6. The formula V= Tr²h gives the volume of a cone with radius r and height h. 3 a) Rearrange the…

A:

Q: Use a known series to find a power series in x that has the given function as its sum: 1. xcos(x³)…

A: Step 1: Problem 1:  Power Series for xcos(x3)We start with the well-known Maclaurin series expansion…

Q: B:Show that the function 4H(x,y)= (x² + y2)2-2((x² + y²) is a first integral of ODES: x=y + y(x² +…

A:

Q: +21 Rsts = R₁ (R+R) Calculate the total system relibility using the given formula including an…

A: Step 1: Step 1: What the Diagram Shows The diagram appears to represent a redundant parallel…

Q: Please show all steps and write out the answer instead of typing it out, thanks

A:

Q: Self-learning linear algebra, solving system of linear equations. Can you solve this exercise to…

A: If you have any problem let me know in the comment section thank you.

Q: Also, construct a know-show table to outline the proof of this proposition.

A: Step 1: Understanding the Proposition We are asked to verify the following claim: For all integers a…

Q: Statement:If 2 | a and 3| a, then 6 a. So find three integers, and at least one integer should be…

A: If you have any problem let me know in the comment section thankyou.