Graphs are useful for comparing relationships. Here are two graphs representing the amount of caffeine in Person A and Person B, in milligrams, at different times, measured hourly, after an initial measurement.

Graph of an exponential function, origin O. Horizontal axis, time (hours), scale 0 to 10, by 1’s Vertical axis, caffeine (mg), scale 0 to 200, by 100’s. The function is discrete and has these approximate points: (0 comma 200), (1 comma 160), (2 comma 125), (3 comma 105), (4 comma 80), (5 comma 65), (6 comma 50), (7 comma 45), (8 comma 35), (9 comma 25), (10 comma 20), (11 comma 18) and (12 comma 12).

Graph of an exponential function, origin O. Horizontal axis, time (hours), scale 0 to 10, by 1’s. Vertical axis, caffeine (mg), scale 0 to 200, by 100’s. The function is discrete and has these approximate points: (0 comma 100), (1 comma 90), (2 comma 80), (3 comma 70 ), (4 comma 65), (5 comma 60), (6 comma 57), (7 comma 50), (8 comma 45), (9 comma 40), (10 comma 38), (11 comma 35) and (12 comma 30).

The graphs reveal interesting information about the caffeine in each person over time:

• At the initial measurement, Person A has more caffeine (200 milligrams) than Person B (100 milligrams).
• The caffeine in Person A's body decreases faster. It went from 200 to 160 milligrams in an hour. Because 160 is $\frac{8}{10}$ (or $\frac45$) of 200, the growth factor is $\frac45$.
• The caffeine in Person B's body went from 100 to about 90 milligrams, so that growth factor is about $\frac{9}{10}$. This means that after each hour, a larger fraction of caffeine stays in Person B than in Person A.
• Even though Person A started out with twice as much caffeine, because of the growth factor, Person A had less caffeine than Person B after 6 hours.