Answers
APM Solutions for Assignment 1 Semester 2
- Institution
- University Of South Africa (Unisa)
APM Solutions for Assignment 1 Semester 2
[Show more]
Seller
Follow
Content preview
APM1514/201/2/2018Tutorial letter 201/2/2018
Mathematical Modelling
APM1514
Semester 2
Department of Mathematical Sciences
Ths tutorial letter contains solutions for assignment 01.
BARCODE
university
Define tomorrow. of south africa
, Solutions to assignment 01
1. (a) From an+1 = a2n , and a0 = 2
for n = 0; a1 = a20 = 22
2 2
n = 1; a2 = a21 = (22 ) = 22
2
2 3
n = 2; a3 = a22 = (22 ) = 22
2 2
2 2 2 4
n = 3; a4 = a3 = (2 ) = 22
! 2
2 2 2
2 = 225
n = 4; a5 = a24 = (22 )
(b) Equilibruim points
from: an+1 = a2n , we have
a = a2
0 = (a2 − a)
0 = a (a − 1)
∴ a = 0 or a = 1
(c)
2
a1 = a20 , a2 = a20 , a3 = a2
4 5
a4 = a20 , a5 = a20
n
(d) an = a20
An
2. (a) A(n+1) = An + 100 − 3000
A(n+1) = 1.01An − 3000
(b) equilibrium point
A = 1.01A − 3000
A
= 3000 ∴ A∗ = 300 000
100
(c) Since A0 = 200 000 < A∗ = 3000 00, it follows that the loan will be paid out completely.
(d) Yes, it will, and will not, for example
(i) will not change,
(ii) yes it will change to
A(n+1) = 1.01An − 1600
(iii) yes it will change to
2
A(n+1) = An + An − 3000
100
2
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through EFT, credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying this summary from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller Maths_stud. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy this summary for R50,00. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
50843 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy summaries for 14 years now