Exponential Growth

Exponential Decay

Example 1 Graph the exponential function given by Solution xy or f(x) 0 1 –1 2 – /3 9 1/9 27

Example 2 Graph the exponential function given by Solution xy or f(x) 0 1 –1 2 –2 –3 1 1/3 3 1/9 9 27

Exponential GrowthExponential Decay

From the previous two examples, we can make the following observations. A. For a > 1, the graph of f (x ) = a x increases from left to right. The greater the value of a the steeper the curve, this is called exponential growth. B. For 0 < a < 1, the graph of f (x ) = a x decreases from left to right. For smaller values of a, the graph becomes steeper, this is called exponential decay. C. All graphs of f (x ) = a x go through the y-intercept (0, 1), and (1, a).

D. All graphs of f (x) = a x have the x-axis as the asymptote. E. If f (x ) = a x, with a > 0, a not 1, the domain of f is all real numbers, and the range of f is all positive real numbers.

Example 2

Example 3

Compounded Interest

Example 4

Examples 5. 6.

Example 7.