Class notes
Written Assignment 1
- Course
- MATH 100
- Institution
- University Of British Columbia (UBC )
In Math 100 of UBC, there is 5 written assignment in total which weigh 20% of your final course.
[Show more]
Content preview
ASSIGNMENT 1Trung Duong Nguyen - 14624761
Syifa Nadhira Nurul Izzah - 63842660
Hussein Al Aaref - 19722024
For a particular species, the model
Rx
f (x) = , M > 0, R > 1
1 + x/M
describes the size f (x) of a population given the size x of the population in the previous generation. Because
x represents a population, the domain is restricted to x ≥ 0.
1. (a) Solve f (x) = x.
Rx
→ =x
1 + x/M
Rx
→ −x=0
1 + x/M
R
→x×( − 1) = 0
1 + x/M
R
→ x = 0 or =1
1 + x/M
→ x = 0 or R = 1 + x/M
→ x = 0 or R − 1 = x/M
→ x = 0 or x = M (R − 1)
(b) Describe in a paragraph what the solution(s) found in part (a) represent, in terms of populations.
- When letting f (x) = x it also means that the population of the initial generation and the past
generation are equal. Getting x = 0 means that if the initial population is 0, then there will be no
growth and the population will remain the same. On the other hand, at x = M (R − 1), we will get
a population where there is no growth, where the number of death and newborns are equal
2. (a) What polynomial function approximates f (x) well for large values of x? Explain your reasoning.
- For large values of x, the denominator of the function can be simplified as x/M since 1 will be too
small compared to x and can be ignored. Therefore the function will become:
Rx
f (x) =
x/M
R
→ f (x) =
1/M
→ f (x) = R ∗ M
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 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 these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller tranghane. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for CA$6.24. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
76449 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now