EMAT 4680 Assignment #23 The Spreadsheet in Mathematics Explorations


#1. Model and explore the following classic problem using a spreadsheet:

What if I offered you the following two choices:

a. I will give you $1,000,000 today. 
OR
b. I will give you a penny today, two pennies tomorrow, 
four pennies the next day and so on for one month.

Which option would you select?


2. Construct a graph of any rational function h(x) = f(x)/g(x) where f(x) and g(x) are polynomials by generating a table of values with the x values in one column and the y values in another. Then using this table of values, calculate the limit of h(x) as x approaches:

a. a positive integer
b. a negative integer
c. a value for which h(x) is undefined
d. positive infinity
e. negative infinity


3. Generate a Fibonnaci sequence in the first column using f(0) = 1, f(1) = 1,

f(n) = f(n-1) + f(n-2)

a. Construct the ratio of each pair of adjacent terms in the Fibonnaci sequence. What happens as n increases? What about the ratio of every second term? etc.

b. Explore sequences where f(0) and f(1) are some arbitrary integers other than 1. If f(0)=1 and f(1) = 3, then your sequence is a Lucas Sequence. All such sequences, however, have the same limit of the ratio of successive terms.

Check it out :)


4. Problem: Place four numbers in the first row as follows

A B C D

For each successive row replace the entries by the absolute value of the difference of the entry just above and the entry just to the right in the previous row. In the fourth position use the absolute value of the difference of the fourth and the first (i.e. cycle)

|A-B| |B-C| |C-D| |D-A|

Will the process lead to a 0 in all 4 entries for some row?

What is the largest number of rows before a zero row is generated?

(If your answer is less than 10, you should try again)


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