Chapter 5 - Recurrence Relations Unit 3

When fully repaid, the loan that will cost Daniel the least amount of money is

• Loan I

• Loan II

• Loan III

• Loan IV

• Loan V

Which one of the following depreciation situations does this graph best represent?

• flat rate with a decreased rate after 2 months

• flat rate with an increased rate after 2 months

• unit cost with a decrease in units used per month after 2 months

• reducing balance with an increased rate after 2 months

• reducing balance with a decreased rate after 2 months

How many dollars does Julie initially invest?

• $12000

• $1.0062

• $12074.40

• $1200

After how many months will the balance of Julie's account first exceed $12 300?

• 5 months

• 3 months

• 4 months

• 6 months

Which could be an appropriate rule to model this situation?

• Balance = 12 000n + 1.0062

• Balance = 12 000 x 1.0062n

• Balance = 1 200 x 1.0062ⁿ

• Balance = 12 000 x 1.0062ⁿ

What is the value of this loan after 5 months?

• $24380.31

• $24706.19

• $25031.10

• $25355.03

• $25678.00

The first five terms of a sequence are 2, 6, 22, 86, 342.

The recurrence relation that generates this sequence could be:

• $P_0=2\ \ \ \ \ \ \ \ P_{n+1}=P_n\ +\ 4$

• $P_0=2\ \ \ \ \ \ \ \ P_{n+1}=2P_n\ +\ 2$

• $P_0=2\ \ \ \ \ \ \ \ P_{n+1}=3P_n$

• $P_0=2\ \ \ \ \ \ \ \ P_{n+1}=4P_n\ -\ 2$

• $P_0=2\ \ \ \ \ \ \ \ P_{n+1}=5P_n\ -\ 4$

A printer was purchased for $680.

After 4 years the printer has a value of $125.

On average, 1920 pages were printed every year during those 4 years.

The value of the printer was depreciated using a unit cost method of depreciation.

The depreciation in the value of the printer, per page printed, is closest to

• 3 cents

• 4 cents

• 5 cents

• 6 cents

• 7 cents

The purchase price of a car was $26 000.
Using the reducing balance method, the value of the car is depreciated by 8% each year.
A recurrence relation that can be used to determine the value of the car after n years,  $C_n$  is

•  $C_n\ =\ 26000,\ \ \ \ \ \ \ C_{n+1}\ =\ 0.92C_n$  

•  $C_n\ =\ 26000,\ \ \ \ \ \ \ C_{n+1}\ =\ 1.08C_n$  

•  $C_n\ =\ 26000,\ \ \ \ \ \ \ C_{n+1}\ =\ C_n+8$  

•  $C_n\ =\ 26000,\ \ \ \ \ \ \ C_{n+1}\ =\ C_n-8$  

•  $C_n\ =\ 26000,\ \ \ \ \ \ \ C_{n+1}\ =\ 0.92C_n-8$  

The amount of payment number 2 that goes towards reducing the principal of the loan is

• $486

• $502

• $504

• $996

• $998