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.

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Presentation transcript:

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.

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

x y y = 2 -x 421½¼421½¼

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

x y y = 2 x+1 ½1248½ ¼ Graph shifted left one.

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

The number ee = … x y 1/e 2 1/e 1 e e 2 = y = e x

Using the One-to-One Property Ex.

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

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