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APM1514 Assignment 4 (COMPLETE ANSWERS) 2024 - DUE 10 June 2024

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APM1514 Assignment 4 (COMPLETE ANSWERS) 2024 - DUE 10 June 2024 ;100 % TRUSTED workings, explanations and solutions. For assistance call or W.h.a.t.s.a.p.p us on ...(.+.2.5.4.7.7.9.5.4.0.1.3.2)........... Question 1: 8 Marks Suppose that the population of South Africa was approximately 60, 04 m...

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APM1514
ASSIGNMENT 4 2024
UNIQUE NO.
DUE DATE: 10 JUNE 2024

, APM1514/101/0/2024




Mathematical Modelling

APM1514

Year module

Department of Mathematical Sciences


Problems: Assignment 4




BAR CODE




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Open Rubric of south africa

, ASSIGNMENT 04
Due date: Monday, 10 June 2024
Total Marks: 100


ONLY FOR YEAR MODULE

This assignment covers study units 5 & 6 in the study guide



Question 1: 8 Marks

Suppose that the population of South Africa was approximately 60, 04 million at the beginning of year 2021,
and that it follows the Malthusian model approximately, with a growth rate of 1.24 percent per year.

(1.1) When will the population reach 70 million, if the growth rate does not change? (4)

(1.2) What does the model predict the population of South Africa to be in the year 2050? (4)


Question 2: 14 Marks


(2.1) Given H = 2 mg/ml, L = 0.5 mg/ml, and k = 0.02 h − 1 , suppose concentrations below L (7)
are not only ineffective but also harmful. Determine a scheme for administering this drug (in
terms of concentration and times of dosage).

(2.2) Suppose that k = 0.3hr − 1 and that the smallest effective concentration is 0.04 mg/ml. A (7)
single dose that produces a concentration of 0.1 mg/ml is administered. Approximately how
many hours will the drug effective?


Question 3: 10 Marks

The populations of Country R and Country U both grow according to the Malthusian model, Country R with
a doubling time 100 years and Country U with a doubling time 120 years. If the sizes of the populations
were the same in year 2000, what was the ratio of the population of Country U to the population of Country
R in 1900? What will the ratio be in 2100?


Question 4: 12 Marks

Which of the following statements are true, and which are false? You must be able to justify your answers!

(4.1) The more there is of a radioactive substance, the greater its rate of decay is. (4)

(4.2) If the growth constants of two Malthusian populations A and B are kA and kB , and if kA = (4)
2 ∗kB , then after 10 years the population A is two times larger than the population B.


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