Department of Mathematics, Statistics
and Computer Science
Wim Ruitenburg's Fall 2014 MATH 1300-101
Last updated: October 2014
Comments and suggestions: Email wimr@mscs.mu.edu
Growth from chapter 9
From Section 9.1 we can learn:
- There are many ways to describe a sequence.
Sometimes very precise but cumbersome.
Sometimes informal and not always clear.
- An example of an unclear sequence: 2, 3, 5, 8, .....
What is the next number?
There is no reasonable and unique correct answer.
From Section 9.2 we can learn:
- What is a linear sequence, also called an arithmetic sequence?
- Given a linear sequence that begins as 7, 13, ..., what is the next
number?
- Quick and easy ways to add a long list of numbers of a linear sequence.
From Section 9.3 we can learn:
- An exponential growth sequence is also called a geometric sequence.
- Exponential growth talks about increasing geometric sequences as well as
about decreasing geometric sequences.
From Section 9.4 we can learn:
- Logistic growth more closely reflects `exponential' growth when we are
bound by limited resources.
Example Problem(s)
-
(This exercise is about why approximate mathematical models are a good thing.)
We have 2 clocks.
The 1st clock stands still, while the 2nd clock runs but is a little bit off.
So the 1st clock is perfectly accurate twice a day, while the 2nd clock is
never accurate.
Give sound reasons why the 2nd clock is better than the 1st.
- Recommended problems from Chapter 9 of the book:
1, 5, 10a, 14a
- Recommended problems from Chapter 9 of the book:
19, 23, 30
- Recommended problems from Chapter 9 of the book:
37ac, 39, 47, 52
- Recommended problems from Chapter 9 of the book:
53a, 56a
- Consider the logistic equation p(n+1) = 4 * p(n) * (1 - p(n) / 1000).
So a = 4 is the growth rate and C = 1000 is the capacity of the environment.
- If p(0) = 1 (which is small), give a decent approximation of p(1).
Does the growth rate look like exponential with ratio 4?
- If p(25) = 500, compute p(26).
- Suppose x = p(55) = p(56) is positive, so the population is stable.
Compute x.