Objective- To use graphs to compare linear expressions. Acme Best C = 250 + 0.01n C = 70 + 0.03n C n Acme Best 500 400 300 200 100 250 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)

Objective- To use graphs to compare linear expressions. Acme Best C = 250 + 0.01n C = 70 + 0.03n C Best n Acme Best 500 400 300 200 100 250 70 70 Acme 2000 270 270 130 130 Cost 4000 290 290 190 190 6000 310 310 250 250 They meet at 9000 copies 8000 330 330 310 310 10,000 350 350 370 370 n 0 2 4 6 8 10 12 Number of Copies (in thousands)

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 d 100 + 2.04 They meet at about 20.4 sec. 4.9 4.9 d 102.04 20.4 t

Tortoise and Hare Race Let t = time in seconds Let d = distance run d = 100 + 0.1t d = 5t t Tortoise Hare 125 100 75 50 25 100 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

Tortoise and Hare Race Let t = time in seconds Let d = distance run d = 100 + 0.1t d = 5t t Tortoise Hare 125 100 75 50 25 Tortoise 100 100 5 100.5 100.5 25 25 Distance 10 100.1 100.1 50 50 15 100.15 100.15 75 75 Hare Looks like 20.4 sec. 20 100.2 100.2 100 100 25 100.25 100.25 125 125 0 5 10 15 20 25 Time