Objective To use graphs to compare

1
Objective- To use graphs to compare linear
expressions.
Acme
Best
C 250 0.01n
C 70 0.03n
C
500 400 300 200 100 0
n
Acme
Best
0
250
70
2000
270
130
Cost
4000
290
190
6000
310
250
8000
330
310
10,000
350
370
n
0 2 4 6 8 10 12
Number of Copies
(in thousands)
2
Objective- To use graphs to compare linear
expressions.
Acme
Best
C 250 0.01n
C 70 0.03n
C
Best
500 400 300 200 100 0
n
Acme
Best
0
70
250
70
Acme
2000
270
130
270
130
Cost
4000
290
190
290
190
6000
310
250
310
250
They meet at 9000 copies
8000
330
310
330
310
10,000
350
370
350
370
n
0 2 4 6 8 10 12
Number of Copies
(in thousands)
3
Tortoise and Hare Race
The tortoise gets a 100 ft. head start and runs
at 0.1 ft/sec. The hare runs at 5 ft/sec. When
does the hare reach the tortoise?
Let t time in seconds
Let d distance run
Tortoise
Hare
d 100 0.1t
d 5t
100 0.1t 5t
d 100 0.1t
- 0.1t -0.1t
d 100 0.1(20.4)
100 4.9t
They meet at about 20.4 sec.
d 100 2.04
4.9 4.9
d 102.04
20.4 t
4
Tortoise and Hare Race
Let t time in seconds
Let d distance run
Tortoise
Hare
d 100 0.1t
d 5t
t
Tortoise
Hare
125 100 75 50 25 0
0
100
0
5
100.5
25
Distance
10
100.1
50
15
100.15
75
20
100.2
100
25
100.25
125
0 5 10 15 20 25
Time
5
Tortoise and Hare Race
Let t time in seconds
Let d distance run
Tortoise
Hare
d 100 0.1t
d 5t
t
Tortoise
Hare
125 100 75 50 25 0
Tortoise
0
100
0
100
0
5
100.5
25
100.5
25
Distance
10
100.1
50
100.1
50
Hare
15
100.15
75
100.15
75
Looks like 20.4 sec.
20
100.2
100
100.2
100
25
100.25
125
100.25
125
0 5 10 15 20 25
Time