Pre-Calculus :Chapter 3.1 Exponential Functions and Their Graphs Mrs.Volynskaya Pre-Calculus :Chapter 3.1 Exponential Functions and Their Graphs The exponential function f with base a is denoted by f(x) = ax and x is any real number.

Graph y = 2x x y -2 -1 1 2 2-2 = 2-1 = 1 2 4

y = 2-x x y -2 -1 1 2 4 2 1 ½ ¼

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

y = 2x+1 x y -2 -1 1 2 ½ 1 2 4 8 -3 ¼ Graph shifted left one.

y = -2x y = 2x x y -2 -1 1 2 -1/4 -1/2 -1 -2 -4 Reflects about x-axis

The number e e = 2.71828… y = ex x y -2 -1 1 2 1/e2 1/e 1 e e2 = 7.389

Using the One-to-One Property Ex.

Formulas for Compound Interest For n compoundings per year: yearly 1 monthly 12 semi-ann 2 daily 365 For continuous compounding:

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 = 12,000e.09(5) A = $18,819.75 A = $18,726.11