1. 3.1 Exponential Functions and Their Graphs The exponential function f with base a is denoted by f(x) = a x and x is any real number.

2. Graph y = 2 x x y -2 0 1 2 2 -2 = 2 -1 = 124124

3. -2 0 1 2 x y y = 2 -x 421½¼421½¼

4. -2 0 1 2 x y 5/4 3/2 2 3 5 y = 2 x + 1 Graph shifted up one.

5. -2 0 1 2 x y y = 2 x+1 ½1248½1248 -3¼ Graph shifted left one.

6. -2 0 1 2 x y y = -2 x y = 2 x -1/4 -1/2 -2 -4 Reflects about x-axis

7. The number ee = 2.71828… -2 0 1 2 x y 1/e 2 1/e 1 e e 2 = 7.389 y = e x

8. Using the One-to-One Property Ex.

9. Formulas for Compound Interest For n compoundings per year: For continuous compounding: yearly1 monthly12 semi-ann2 daily365

10. Ex.A total of $12,000 is invested at an annual percentage rate of 9%. Find the balance after 5 years if it is compounded a. quarterly b. continuously A = $18,726.11 A = 12,000e.09(5) A = $18,819.75