# Foundations of Advanced Algebra Name

 Date conversion 22.12.2017 Size 162.39 Kb.

Foundations of Advanced Algebra Name ______________________________________

Selling Credit Cards

Credit card companies pay the people who collect applications for credit cards. They also pay the people who contact current cardholders to sell them additional financial services.

1. For collecting credit card applications, Barry’s daily pay B is related to the number of applications he collects n by the rule B = 20 + 5n.

a) Use the function rule to complete this table of sample (n, B) values:
 Number of Applications 0 1 2 3 4 5 10 20 50 Daily Pay (in dollars)

b) How much will Barry earn on a day when he does not collect any credit card

applications? Explain how you know.

c) How much additional money does Barry earn for each application he collects?

Explain how you know.

d) Write a sentence or two that explains how Barry’s daily pay changes with each new
credit card applications he collects.

2. Cheri also works for the credit card company. She calls existing customers to sell them additional services for their account. The next table shows how Cheri earns for selling selected numbers of additional services.

d) Write a sentence or two that explains how Cheri’s daily pay changes with each additional service she sells.

3. The diagram below shows graphs of pay plans offered by three different banks to employees

who collect credit card applications.

I

II

III

Atlantic Bank: A = 20 + 2n

Boston Bank: B = 20 + 5n

Consumers Bank: C = 40 + 2n

a. Match each function rule with its graph. Explain how you can make the matches

without calculations or graphing help.

b. What do the numbers in the rule for the pay plan at Atlantic Bank tell you about the

relationship between daily pay and the number of credit card applications collected?

1. a)

 Number of Applications 0 1 2 3 4 5 10 20 50 Daily Pay (in dollars) 20 25 30 35 40 45 70 120 270

b) The y values in the table increase by 5 for each increase by 1 of the n values. The graph

shows a vertical increase of 10 for every horizontal increase of 2 which is equivalent

to the change in the table.

c) For 0 credit card applications collected, Barry will still be paid \$20. This is shown in the

rule by the number 20, the constant term; in the table by the entry (0, 20); and in the

graph by the y-intercept (0, 20).
d) Barry earns an additional \$5 for each credit card application he collects. This is shown

by the coefficient of n in the rule, in the table by the increase of 5 in pay for each

increase of 1 in the number of applications, and by the slope of the graph points (up 10

for every 2 units over from one point to the next on the graph).

e) NEXT = NOW + 5; starting at 20
2. a) Cheri’s pay plan seems to be linear because for every additional 10 services sold, her pay

goes up \$20. (Encourage students to plot the points to determine linearity if they

are not sure).
b)

40

70

90

240

242

c)
 Change in Sales Change in Pay (in \$) Rate of Change (in \$ per sale) 10 to 20 20 20 = 2 per sale 10 20 to 25 10 10 = 2 per sale 5 24 to 40 30 30 = 2 per sale 15 50 to 100 100 100 = 2 per sale 50

Notice that the rate of change in pay is always \$2 per sale.
d) NEXT = NOW + 2; starting at 40
e) i. The only rule that is correct is C = 40 + 2n. Reasoning might simply point out that the

other rules don’t give (n, C) pairs like those in the table in part a.

ii. The 40 is the pay with no sales, and the 2 is the amount of additional pay for each sale.
3. a) Graph I matches Boston Bank because it rises the fastest.

Graph II matches Consumers Bank because it rises at the same rate as Atlantic Bank,

but grater y-intercept.

Graph III matches Atlantic Bank because it rises at the same rate as Consumers, but

lower y-intercept.
b) The Atlantic Bank pay rule A = 20 + 2n shows that workers there will be a base pay of \$20

whether or not they collect any credit card applications and an additional \$2 for each

card application they collect.