Algebra 1 Unit 2 Lesson Models
Name:_______________________________
Date:________________________________
Comparing Linear and Exponential Models
You have been given the opportunity to participate in one of two games shows. The first game
show, “Let’s Price That,” awards an initial prize of $25 and increases by $5 each week for twenty
weeks. The second game show, “Spin that Wheel,” awards an initial prize of $.10 and doubles each
week for twenty works.
1) Write a sentence below describing each model.
Model 1:
Model 2:
2) Make a prediction about which model you believe will yield the greatest Cash Prize and explain
your reasoning. Develop your own strategy that would best represent your prediction. Use as
many models needed to help you.
3) Use your strategy to determine how many weeks Model 2 awards a higher cash prize then
model 1.
4) What would be the Cash Prize after 25 weeks for each model. Make a prediction.
Model 1:
Model 2:
EXTENSION:
5) “Let’s Price That” decided to change their Cash Prize to $250 for the initial prize and $50 for
each week. How does this change their model?
6) Which Game show would you want to participate in and why?
Algebra 1 Unit 2 Lesson Models
Name:_______________________________
Date:________________________________
Comparing Linear and Exponential Models
You have been given the opportunity to participate in one of two games shows. The first game
show, “Let’s Price That,” awards an initial prize of $25 and increases by $5 each week for twenty
weeks. The second game show, “Spin that Wheel,” awards an initial prize of $.10 and doubles each
week for twenty works.
1) Write a sentence below describing each model.
Model 1: Initial prize of $25 and increases by $5 each week for twenty weeks
Model 2: Initial prize of $.10 and doubles each week for twenty weeks.
2) Make a prediction about which model you believe will yield the greatest Cash Prize and explain
your reasoning. Develop your own strategy that would best represent your prediction. Use as
many models needed to help you explain.
I think that model one is the best choice because it starts off with more money.
I think that model two is the best choice because it is doubling and will increase faster.
Week
MODEL 1
MODEL 2
Number
Cash Prize Awarded
Cash Prize Awarded
Red represents the regular model, green represents the
Extension at the end.
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Model 1: 25 + 5n
Model 2: .10(2)x
25
30
35
40
45
50
55
60
65
70
75
80
85
90
95
100
105
110
115
120
125
250
300
350
400
450
500
550
600
650
700
750
800
850
900
950
1000
1050
1100
1150
1200
1250
.10
.20
.40
.80
1.60
3.20
6.40
12.80
25.60
51.20
102.40
204.80
409.60
819.20
1638.40
3276.80
6553.60
13,107.20
26,214.40
52,428.80
104,857.60
3) Use your strategy to determine how many weeks Model 2 awards a higher cash prize then
model 1.
At week 10 Model 2 starts to have a higher cash prize.
4) What would be the Cash Prize after 25 weeks for each model. Make a prediction.
Model 1: 25 + 5(25) = $150
Model 2: .10(2)25 = $3,355,443.20
EXTENSION:
7) “Let’s Price That” decided to change their Cash Prize to $250 for the initial prize and $50 for
each week. How does this change their model?
Refer to the green numbers on the chart.
I would still keep with my prediction because Model 2 starts making more money after week 14.
8) Which Game show would you want to participate in and why?
I would participate in the second game show because I could win more money.
I would participate in the first game show because I do not think that I could win more then 10
weeks in a row.
410
390
370
350
330
310
290
270
250
230
210
CASH PRIZE
190
170
150
130
110
90
70
50
30
10
1
3
5
7
9
11
13
15
WEEKS
17
19
21
23
25