Assignment, pencil, red pen,
highlighter, textbook, GP notebook,
graphing calculator
Jon started working at See’s candies. On the 5th day of
the job, Jon ate 15 pieces. On the 11th day he ate 27
pieces. Based on this arithmetic pattern,
a) How many candies did Jon eat initially?
b) Write the general rule t(n).
c) On what day did Jon eat 45 candies?
total:
10
Jon started working at See’s candies. On the 5th day of
the job, Jon ate 15 pieces. On the 11th day he ate 27
pieces. Based on this arithmetic pattern,
a) How many candies did Jon eat initially?
n
5
11
t(n)
15
27
+1
+1
Common  27  15  12
2
difference 11  5
6
b) Write the general rule t(n).
total:
10
t(n) = dn +b
15 = 2(5) + b +1
+1
15 = 10 + b
Jon initially ate 5
5 = b +1
candies.
t(n) = 2n + 5 +2
c) On what day did Jon eat 45 candies?
45 = 2n + 5 +1
40 = 2n
20 = n +1
+1
Jon ate 45 candies on the 20th day.
BB – 85
Starting with x in each case where x represents the original
cost, find a simplified form for each increase or decrease.
i) a 30% increase
100% + 30%
= 130%
= 1.30x
ii) a 5.2% decrease
100% – 5.2%
= 94.8%
= 0.948x
a) a 5% increase
100% + 5%
= 105%
= 1.05x
b) a 12% discount
100% – 12%
= 88%
= 0.88x
c) a 8.25% tax
100% + 8.25%
= 108.25%
= 1.0825x
d) a reduction of 22.5%
100% – 22.5%
= 77.5%
= 0.775x
BB – 86
Remember the flu epidemic in BB–75? It has become a statewide
crisis, but you have also developed a deeper understanding of how a
multiplier can help you solve a problem such as this.
…
a) If Dallas has 1250 cases at the start of the epidemic, with an
increase of 27% per week, how many cases would be reported in Dallas
after four weeks of the epidemic?
4
Initial
value
=
1250
t(4)
=
1250(1.27)
n t(n)
t(4)  3252 cases
Multiplier = 100% + 27%
0 1250
= 127%
1 1588
= 1.27
2 2016
b) Write the general expression from which you can
3 2560
determine the number of cases in any week of the
4 3252
Dallas flu season.
t(n) = 1250(1.27)n
n
n 1250(1.27)
BB – 86
n
t(n)
0
1
2
3
4
5
6
7
8
1250
1588
2016
2560
3252
4130
5245
6661
8459
c) If Health Services provided 8000 doses of an
experimental medication to fight the virus, when will the
medication be used up (assume one dose per person
affected)?
t(n) = 1250(1.27)n
8000 = 1250(1.27)n
1250
1250
6.4 = (1.27)n
Do you have any ideas how to solve this problem????
We cannot solve for the unknown exponent!
Let’s just continue the table until we surpass 8000.
The medication will be used up at about the 8th week.
1. You and your friend’s favorite shoe store is having a going-out-ofbusiness sale. Sign are posted around the store that state 25% is
taken off each day off the cost of items for four straight days.
Your friend found a pair of $100 shoes. He decides to wait until the
last day to buy the shoes because he thinks that by the 4 th day, the
shoes will be free. You tell him that the shoes will not be free on the
4th day.
Explain your reasoning to your friend. Your work and explanation
should involve the mathematical concepts used in this chapter.
Initial value = $100
t(n) = 100(0.75)n
Multiplier = 100% – 25%
t(4) = 100(0.75)4
= 75%
t(4)  $31.64
= 0.75
My friend added 25% per day, but he should multiply the
percentage to determine the cost.
The shoes will cost $31.64 on the 4th day.
2. You are offered the position of CEO for 2 different companies.
•Company A pays $250,000 per week.
•Your pay rate for Company B is 1¢ for showing up to work on the first
day, then the amount doubles per week. For instance, your pay rate
for Company B is 2¢ for one week of work, 4¢ for 2 weeks of work, 8¢
for 3 weeks of work, 16¢ for 1 month of work, and so on. The
company pays you nothing until the end of 8 months. You get paid
whatever the current weekly pay rate is at that time.
Which plan would you chose? Show your reasoning to support your
decision. Tables are provided below to assist you with your decision.
Company A pays $250,000 per week.
Company A
Initial value = 0
Common difference = $250,000
time: 8 months
# of weeks = 8(4) = 32 weeks
t(n) = 250,000n + 0
t(32) = 250,000(32) + 0
t(32) = $8,000,000
The total pay for 8 months
of work at Company A is
$8,000,000.
Your pay rate for Company B is 1¢ for showing up to work on the first
day, then the amount doubles per week. For instance, your pay rate
for Company B is 2¢ for one week of work, 4¢ for 2 weeks of work, 8¢
for 3 weeks of work, 16¢ for 1 month of work, and so on. The
company pays you nothing until the end of 8 months. You get paid
whatever the current weekly pay rate is at that time.
Company B
Initial value = 0.01
Multiplier = 2
time: 8 months
# of weeks = 8(4) = 32 weeks
t(n) = 0.01(2)n
t(32) = 0.01(2)32
t(32) = $42,949,672.96
The total pay for 8 months of work at Company B is $42,949,672.96.
In the long run, Company B pays more than Company A.
BB – 84
Karen works for a department store and receives a 20% discount on any
purchases that she makes. Today the department store is having the end
of year clearance sale where any clearance item will be marked 30% off.
When Karen includes her employee discount with the sale discount, what is
the total discount she will receive? Does it matter what discount she takes
first? Answer the following questions to find out.
Using graph paper, separate two 10 x 10 grids as shown below.
Case #1: 20% discount first
Case #2: 30% discount first
BB – 84
Case #1: 20% discount first
Case #2: 30% discount first
100(0.2) =
100(0.3) =
20 squares
30 squares
a) Each grid has 100 squares – take the first discount in each case by
shading the appropriate number of squares.
i) How many squares remain after the first discount in case #1?
80 squares remain after the first discount.
ii) How many squares remain after the first discount in case #2?
70 squares remain after the first discount.
BB – 84
Case #1: 20% discount first
Case #2: 30% discount first
80 (0.3) =
70 (0.2) =
24 squares
14 squares
b) Using the remaining squares in each case take the second
discount. Note: you no longer have 100 squares to start!
i) How many squares remain after the second discount in case #1?
56 squares remain after the second discount.
ii) How many squares remain after the second discount in case #2?
56 squares remain after the second discount.
BB – 84
Case #1: 20% discount first
Case #2: 30% discount first
c) When you take a 20% discount, what percent is left?
100% - 20% = 80%
d) When you take a 30% discount, what percent is left?
100% - 30% = 70%
e) Multiply these results together. What percent do you have now?
How does this relate to Karen’s problem above?
(80%)(70%) = (0.8)(0.7) = 0.56 = 56%
The answer is the same as part (b). It does not matter which
discount is taken first.
BB – 87
A local real estate developer decides to hire 2 high school students to
rake the leaves along a green belt. They will work a couple hours each
afternoon until the job is completed. The job is expected to take about 3
weeks. They can choose one of two payment plans:
 Plan A pays $11.50 per afternoon
 Plan B pays 2 cents for one day of work, 4 cents for two days of
work, 8 cents for 3 days of work, a total of 16 cents for four days, and
so on.
Each student chooses a different plan. On which day would their pay
be approximately the same? Support your thinking with data charts
and/or graphs.
BB – 87
Plan A
 pays $11.50 per afternoon
Let n represent
the number of
days worked.
n
t(n)
0
1
2
3
4
5
0
11.50 Let t(n) represent
the total money
23.00 earned on the job.
34.50
46.00 Plan A starts at $0
since no work is
57.50 done initially.
…
n
11.50n + 0
t(n) = 11.50n
n
t(n)
0
1
2
3
4
5
0
0.01
0.02
0.04
0.08
0.16
0.32
The pay doubles
every day.
Even though the person
is not paid for just
showing up initially, what
would the initial value be
hypothetically based on
the doubling pattern?
…
t(n) = 11.50n + 0
Plan B
 pays 2 cents for one day of
work, 4 cents for two days of work, 8
cents for 3 days of work, a total of
16 cents for four days, and so on.
n
0.01(2)n
t(n) = 0.01(2)n
BB – 87
Type both equations into you graphing calculator as:
Plan A:
t(n) = 11.50n
Y1 = 11.50x
Plan B:
t(n) = 0.01(2)n
Y2 = 0.01(2)x
Go to TABLE
to view the values for each function.
Answer the question:
On which day would each student’s pay be approximately the same?
In 14 days they will earn close to the same amount.
BB – 88
You favorite radio station, WCPM, is having a contest. The D.J. poses a
question to the listeners. If the caller answers correctly, he/she wins the
prize money. If the caller answers incorrectly, $20 is added to the prize
money and the next caller is eligible to win. The question is difficult and
no one has won for 2 days.
a) You were the 15th caller today and you won $735!! How much was
the prize worth at the beginning of today? Be careful; think about how
many times the prize was increased today.
b) Suppose the contest starts with $100. How many people would
have to guess incorrectly for the winner to get $1360?
BB – 88
a) You were the 15th caller today and you won $735!! How much was
the prize worth at the beginning of today? Be careful; think about how
many times the prize was increased today.
n
t(n)
0
1
2
3
4
5
6
7
8
9 10 11 12 13 14 15
+20 +20 +20 +20 +20 +20 +20 +20 +20 +20 +20 +20 +20 +20
735
Original prize = $735 – 14($20)
= $735 – $280
= $455
b) Suppose the contest starts with $100. How many people would have
to guess incorrectly for the winner to get $1360?
t(n) = 20n + 100
Initial value = $100
1360 = 20n + 100
Common
63 people would have
= $20
1260
=
20n
Difference
to guess incorrectly.
n = 63