1.) a.) The graph below is a plot of the terms of a difference equation of the f

Question

1.)

a.)

The graph below is a plot of the terms of a difference equation of the form

yn+1 = a yn + b.

From the following list of descriptions, pick the term, or terms, that apply to the graph.

Do this for the graph (figure 2), picking the term, or terms, that apply.

-constant

-increasing

-decreasing

-monotonic

-oscillatory

-unbounded

-asymptotic to the line

b.)

Suppose that you borrow 200000 dollars from a bank, and that the bank charges 4 percent annual interest, compounded monthly, on the loan. You make monthly payments of 150 dollars at the end of each month.

Write down a word equation that can be used to calculate the amount that is owed on the loan at the end of the month in terms of the amount owed at the start of the month.

Writing the monthly balance (i.e. how much is owed) as yn , translate your word equation into mathematical terms. Simplify this equation.

If we write

yn+1 = a yn + b

What is a?

Explanation / Answer

This is certainly not constant as
if it were, then all the points would like on a horizontal line

This is certainly not increasing because from the first to second point
the function is decreasing

Not decreasing because from the second to third point, the function
is increasing

Not monotonic because it is not ONLY decreasing or ONLY increasing

OScillatory ----> absolutely

Unbounded -----> absolutely because if the next few points were drawn,
then we'd get it to keep going further and further up and down

Asymptotic to the line ----> No because it is not approaching a particular line as x ----> infinity

So, answers :
oscillatory , unbounded

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