Drawing Growth

The dashed line $y = 3x$ is above the curve $y = {2}^{x}$ at x = 1, 2 and 3. At x = 5, the curve is at 32 and the line is at 15. Multiplying grows much faster than adding.

Two points are enough to draw $y = a\cdot {b}^{x}$: (0, a) and (1, a times b). If b is more than 1, the curve goes up. This is growth. If b is between 0 and 1, the curve goes down. This is decay. b is never negative and never 1.